*‘FlTl—f-Tru—g—.

INDUSTRIAL TIME REDUCTION CURVES AS
TOOLS FOR FORECASTING

Thesis for the Dagm of Ph. D.
MICHIGAN STATE UNIVERSITY
S. Alexander Billon
1960

LLM LLLLLLL L. .

3 1293 01079 7094

This is to certify that the
thesis entitled l

INDUSTRIAL TIE-1E REDUCTION UIVES

I
AS TOOLS FOR FORECASTING - . I
presented by

8. Alexander Billon

has been accepted towards fulfillment l
of the requirements for

degree in_BL;§. Adm. l

4
v ~- e m ”:1 14L x 2 210%

Major prefessor
Date 4M—

0-169

m It mum DOXtonmovotnlaohookouflunywrncoM.
TO AVOID FINES return on or bdoro data duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU la An Affinnatlvo Action/Emu Opportunity Institution
Wm:

 

INDUSTRIAL TIRE REDUCTIOH CUAVES AS

t-II

COLS FOR FORECASTIIO

Submitted to the School for Advanced Graduate Studies of
Kichigan State University of Agriculture and

Applied Science in partial fulfillment of
the requirements for the degree of

DOCTOR OF PETLCSOPIY

Department of Personnel and Production Administration

1960

ABSTRACT
IIDUSTR AL TIKE iZDUCTIOX CURVES
The purpose of this study is to determine the reliability of the

time reduction curve as a tool for forecasting direct ran-hours required

in manufacturing. The time reduction curve is defined as the relation-

ship in which the cumulative average direct man-hours per unit used in
the manufacture of a product tend to decline by a constant percentage
as the cumulative quantity produced is doubled. Where this relationship
is present, it may be represented by a straight line on double log-
arithnic scale.

Historical direct man—hour data, consumed at various cumulative
quantities of output, were obtained from three manufacturers. The data
represents fifty-four products, and five production programs.

The following questions relative to the time reduction curve were
investigated:

First, does the time reduction curve phenomenon exist in situations

other than those where production is based.on a predetermined time reduc—
tion curve? It has been suggested that the curve's existence in the air—
frame industry is a result of acceptance of this phenomenon as a valid
relationship.
Analysis of empirical data strongly sugaests that the existence

of the time reduction curve phenomenon is not predicated on the use of
the curve for purposes of planning and control of man—hours required in
production.

The firms, from which data were obtained, did not employ a

preconceived model of time reduction, yet a definite regularity in time

-1-

-2-

reduction was observed in a majority of cases.

Second, what is the reliability of the linear form of the time

reduction curve on log-log scales?

The correlation to the least squares computed line of regression
is high. In fifty of fifty—four cases the index is greater than .90.
Over 8h per—cent of the time reduction curves computed were found to
be reliable, e.g. did not exceed an arbitrarily set standard of re—
liability of 4 per-cent standard error of estimate.

Third, what is the magnitude of variation in the rate of time

reduction among firms manufacturing similar products, non-similar

products made by one firm, and various models of a basic product type

manufactured by one firm?

In every category of production the variation in slope exceeded
6 per—cent. The variations in curve slope are of such magnitude as to
limit seriously the usefulness of slope experienced on past models when
determining what slope should be used in forecasting man-hours of future
models of a product type.

Fourth, is it possible to estimate the applicable rate of time
reduction on the basis of man—hour data observed in the manufacture
of an initial quantity of a product?

A mathematical formula which gives the exact number of observa-

tions required before slope characteristic of certain confidence may

be determined has been proposed. ‘Uhen this approach to the estimating

of time reduction curve slope is used, it is recommended that for the

quantity required for slope estimating, man-hour data be reported on

-3-

the basis of units or small lots.

This appears desirable because in cases where the data is reported

on a lot basis the quantity produced may have to be so large as to negate

most of the usefulness of the time reduction curve.

An attempt was made to estimate the slope on the basis of a minimum

of man—hour observations at various quantities. In twenty—two of the

twenty-eight cases it was possible to obtain a relatively accurate fore-

cast of the applicable slepe from three lot values. Four lot values

were used in three cases, and the remaining three cases required five

man—hour values. The average error in the slope estimate, based on

minimum production quantities, for all twenty—eight cases is 1.3 per—cent.
The estimated rate of time reduction was used to forecast man—hours

for various quantities for which actual data were available. Comparison

of the estimited and actual man—hours was made, and the error in estimate

computed. An error in estimate of less than 7 per—cent was obtained in

72.3 per—cent of the fifty-four cases for which computations were made.

T . _ 1 0 a u .
in 90.3 per-cent of cases tne error in man—hour estimate is less than
13 ier—cent. However, in 7.h per—cent of cases the error in estimate

ranges from 20 to 25 per-cent.

Finally, does the time reduction curve have value in forecasting

of man-aours required in production?

It is concluded that in Spite of the fact that the time reduction

curve relationship is highly reliable, it is of limited usefulness in
forecasting direct man-hours required in the production of a product

before a number of units of that product have been manufactured. This

an”.
u

..c’ .1

 

.-
'-o. .
'... _
.. D
.—
'-

 

‘Ll"

condition exists because of the inability to estimate the appli-
cable time reduction curve slepe before the start of production.
Hewever, this study indicates that the time reduction curve is
within certain limitations, a useful tool for forecasting
direct.manéhours required in production after a limited
quantity of a product has been manufactured.

The conclusions of this study are limited by the fact
that data used in the primary analysis were obtained from only
three manufacturers. This was supported, however, by certain

other data reported in the airframe industry.

’3 ”:"TTN “T7
-Lg" - JL‘J—J

The writer wishes to express appreciation to manyibr the
encouragement and assistance during the preparation of the thesis.

In particular, the guidance and assistance provided by
Dr. Rollin K. Simonds, as advisor throughout the thesis, is freatly
appreciated. The time and assistance of Dr. Stanley 3. firyan and
Dr. John H. Hoagland has also been of great value.

The consultation of the several industrial firms has contributed
to the preparation of this study.

I am grateful to Hrs. Amy Coon who so patiently assisted in

typing the study.

“3

U)

Tithout my wife, Irene, who assisted me with editing and w
a source of constant inspiration, this study might never have been
I" ’ 1. 1
llnlSneQ.

Only the writer is responsible for conclusions or inaccuraC1es

that may have crept into this study.

3. Alexander Billon

—iii-

PREFACE
LIST OF
LIST or

Chapter

I.

II.

m n h
i A:)LL'JS o o o o o o o o o o o o o o o o o o o o o

ILLUSTRATIONS . . . . . . . . . . . . . . . . .

IXITRODLICTIOII o o o o o o o o o o o o o o o o o 0

Use of the Time Reduction Curve
Purpose of the Study

[ISTORY AID DEVELOPKEIT OF THE TIRE REDUCTIOK

CUUW
U4 0 o o o o o o o o o o o o o o o o o o o 0

Introduction

The Individual Learner's Curve

The Development of the Time Reduction Curve
Theory

The Orthodox Formulations of the Time Reduction
Curve Theory

J. R. Crawford

Other Contributions

A. B. Berghell

I. M. Laddon

Bureau of Labor Statistics Studies

The Liberty Vessel Study

'Wartime Shipbuilding Study

wartime Productivity Changes in the Airframe
Industry

Daniel W. Carr

Time Reduction Curves in Great Britain

The Hirsch Study

The Reno Cole Survey

Stanley E. Bryan

'World war II Acceleration of Airframe
Production

Company Publications

The Rand Studies

The Stanford Studies

Summary

-iv-

Page

iii

13

TABLE OF COHTERTS - Continued

Chapter

III.

IV.

VI.

VII.

THEORETICAL CONSIDERATION OF THE TIIE REDUCTIOH
CURYJE O O O O O O C O O O O O O O O I O O O O O

The Time Reduction Curve Theory

Assumptions

The Time Reduction Curve on Arithmetic Paper
The Time Reduction Curve on Log—Log Paper
The Boeing Unit Average Curve Concept

The Wright Cumulative Average Curve Concept
The Alternative Time Reduction Curve Concepts
Comparison of Curve Characteristics
Estimating Results Comparison

A hethod of Unit Curve Deviation

Summary and Conclusions

TIIE REDUCTIO:I CUILVE DATA 0 o o o o o o o o o 0

Introduction

hethod of Obtaining Data
Nature 0 Ran—Hour Data
Data Reliability
Summary

RELIABILITY OF THE TIRE REDUCTIOR CURVE . . . . .

Introduction

Pattern of Time Reduction

The Linearity of the Curve

Departures from Linearity

Some Reasons for Departures from Linearity
Summary and Conclusions

ESTIMATING THE RATE OF TILE REDUCTIOH . . . . .

Introduction

Uniformity in Slope

Method of Slope Prediction
Estimating from Initial Quantity
Summary and Conclusions

SOHE FACTORS AFFECTIIG SLOPE . . . . . . . . . .

Introduction
Manual Dexterity and Group Skills
Some Long Range Factors
The Effect of Scale of Production
han_Hours Required and Type of Product
hanagement Learning
Summary and Conclusions
_V_

Page

65

96

123

141

157

TABLE OF COITEETS — Continued
Page
Chapter
VIII. THE PROBLEM OF DESIGN CHANCE . . . . . . . . . . 169

Introduction

Some Theoretical Aspects of Transfer

Present Industrial Lethods for Estimating the
Effect of Changes

Individual Company Practice

An Improved hethod of Estimating the Effects
of a Product Change

Summary and Conclusion

IX. SILIARY AID COXCLUSIOKS . . . . . . . . . . . . . 192

Summary
Conclusions

APPEIDIK . . . . . . . . . . . . . . . . . . . . . . . .

N
C)
\A)

(J\

BIBLIOGRAPIY . . . . . .

o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
(\J
{\J

—Vl-

Table

N
o
H

2.2

3.1
3.2
3.3
3.4
3.5
3.6

4.1

U1
H

5.2

5-3

5.4

5.5

6.1

CO
1...:

CO
C
N

LIST OF TABLES

Survey of Cost—Quantity Technique Utilization

Average Time Reduction Curve Slope for World
war II Airframe Production . . . . . . . . . .

Hypothetical Time Reduction Curve Values. . . . .
Values for the Boeing Unit Curves . . . . . . . .
Values for Wright Time Reduction Curves . . . . .
Alternative Time Reduction Curve Characteristics
Comparison of Actual to Estimated Ran—Hours . . .

Factors Showing the Relationship Between the
Cumulative Average and the Unit Curve . . . .

Through 4.54 Direct Kan—Hour Data . . . . . . . .

Summary of Curve Characteristics, Firm A, Program

LO. 1 o o o o o o o o o o o o o o o o o o o .

Summary of Curve Characteristics Firm A, Program

:70 o 2 o o o o o o o o o o o o o o o o o o o 0

Summary of Curve Characteristics Firm P Program

3:0. 3 O O O C C O O O O O O O O I O O O O O 0

Summary of Curve Characteristics Firm C, Program
::00 1+ O O 0 O O O 0 O O O O C O O O O I 0 I 0
Summary of Curve Characteristics Firm C, Program

2:0 0 5 O O O O O O O O O O O O O O I O O O O 0

Percentage Slope of Typical World'flar II Time
Reduction Curves . . . . . . . . . . . . . .
Comparison of Actual vs. Estimated, Ian—
and Rate of Time Reduction . .

5‘
5:
pg:
(D

O O O O O O 0

'71? "‘L 1 v' Y
The Effect of Product Change on nan—hours

Summary of Kethods of Estimating Change . .

-vii-

O
O

’3
I\)

106

125

126

27

12"}

151
175
132

LIST OF ILLUSTRATI TS

Figure Page
1.1 The Time Reduction Curve on Arithmetic Scale 3
1.2 The Time Reduction Curve on Log-Log Scale . . 4
2.1 A Typical Learner's Curve . . . . . . . . . . 15
2.2 Two Industrial Learning Curves. . . . . . . . 18
2.3 ‘Wright Production Improvement Curves. . . . . 24
2.4 Time Reduction Curves, Selected.Plants. . . . 35
2.5 An S Shape Time Reduction Curve . . . . . . . 39
2.6 weighted Average Total Direct Kai—hours Per

Pound of Airframe All Lodels . . . . . . . 43
2.7 Kan—Hours Per Pound of Airframe All Podels

and Fighters . . . . . . . . . . . . . . . 49
2.3 What is a Kan—Hour. . . . . . . . . . . . . . 53
3.1 An 80 Per-Cent Time Reduction Curve . . . . . 67
3-2 An 30 Per-Cent Cumulative Average Curve . . . 70
3-3 Boeing Time Reduction Curves. . . . . . . . . 74
3-4 'Uright Time Reduction Curves. . . . . . . . . 7?
3-5 Comparison of Wright and Boeing Curves. . . . 79
3-7 Computed Unit and Cumulative Average Curves . C
5-1 Summation of Changed and Unchanged han-Kours. 176
5-2 The Work Added Curve . . . . . . . . . . . . 36
5-3 The Unchanged werk Curve. . . . . . . . . . . S7
5-4 The Composite Time Reduction Curve . . . . . 183

4.1 Through n.23 Fifty—Four Empirical Time

Reduction Curves . . . . . . . . . . . . . 203
_viii-

CHAPTER I

INTRODUCTION

 

Shortly before World Uar II the time reduction curve technique
was developed and used by the Airframe industry and the United States
Air Force for the purpose of planning and controlling the various re-
quirements of defense production programs. For more than two decades
the technique has been known by various names. There is, as yet, no
agreement as to what term should be applied to the technique. Today

. . . . . 1 . 2
this technique is known as the time reduction curve, learning curve,

. 3 . 4 5
experience curve, improvement curve, and progress curve. Of the
various designations used the expression "time reduction curve" seems
to represent the relationship more accurately and is less confusing
than the other names. This expression is broad enough to include the
various factors which have an influence on manufacturing time reduc—

tion. Some of the other designations are either too restrictive or

have previously been adapted to denote other phenomena than that which

 

Douglas Aircraft Company uses this term, see: H. W. Thue,
"Time Reduction Curves,” Proceedings, Industrial Engineering Institute,
University of California, Los Angeles, (1953), p. 26.

 

The term "learning curve" is used by the U. S . Air Force and a
number of contractors. See Air Eateriel Command, Air Force Guide for
Eglgggg, (Dayton, Ohio, November, 1959), p. 35.

3A. J. horgan, Experienge Curves Applicable 39 the Aircraft
Industry, (Baltimore, Maryland: The Glenn L. hartin Company, 1952).

 

. ‘H. F. Brown, The Improvement Curve, (Wichita, Kansas: Boeing
Airplane Company, 1955).

 

5A. Anzanos, et. a1., Contract Estimating Progress Curves, and

3

Application, (St. Louis? thonnell Aircraft Corporation, 1958).

 

-1...

 

 

 

will be presently discussedé.

Because the time reduction curve represents the production pro-
gress in dynamic terms, it has become one of th most important tools
in airframe production analysis as well as cost estimating and pricing
of defense contracts. In the past the use of the time reduction curve
technique has been confined to the airframe industry, its suppliers,
and the Air Force. During the past few years companies engaged in
civilian production are increasing the use of this technique in the
solution of their problems.

The conventional time reduction curve theory, the one most widely
accepted, states that as the quantity produced doubles, the direct
man-hour time per unit declines by a constant percentage7. The term
"time per unit" is often used interchangeably to mean either the
average time of a given number of units or the time of a Specific
unit. The former may be called the cumulative average time reduction
curve and the latter the unit time reduction curve. Both values,
when plotted, represent a hyperbolic function on arithmetic scales.
When the same data is plotted on logarithmic scales a linear function
is obtained. Figures 1.1 and 1.2 show a unit curve of eighty per cent
SIOpe, which shows a cumulative average per unit time reduction of 20
per cent everytime the total quantity produced is doubled. The time
reduction curve theory is based on the hypothesis that the time of
producing an item will decrease as successive units are produced, and

/

o . . . - a - . . - ”x.y
For the origin of tne "learning curve,“ see Chapter 2.

7 m

l. P. Wright, "Factors Affecting the Cost of Airplanes," Jour—
IEl OggAeronautical Sciences, (Feb., 1936) p. 12H.

 

- --—7

lkrtwfib CFH.+LWIKQP Q

\

r 3+

1...

T

 

*-- -_¢. -—-~

v--—--~

-o- -—- ___.,___.._._,

r-

I )ll

.r a

 

 

 

nl.)|‘ It

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

loom ; a

{.1 v .
.. 2.... Zul.

. .. 1.. c.
I -._III lbs!

 

 

 

 

that the amount of the decrease will so es3 with each consecutive
unit. The slope of the curve is usually expressed as a percentage,
e.g., 30 per—cent, 9O per—cent, etc. The slope of the time reduction
curve is simply an expression of the ratio between the man-hours at
anv unit and the man—hours at twice the quantity of that unit. Tne

curve indies We a relatively high rate of decrease at the oaginning

o
H:
St

sequence, but as output is continued, it aporoacnas :0ilitJ,
0

all practical purposes.‘ In theory the decrease in man-

(1)
C—fo
H
(D
07
(Q
(+-
“3

hours continues indefinitely, but as large quantities are prrduced,
the decrease per unit becomes very small and insignificant.

There are mzn/ variaales that r:y contr.:uee to the lecrease in
nan-hours revui red in production. It should not be assumed that all
factors are known or have been isolatel.A1though this could cor—

. ‘ "7" " "‘~ I‘ r "‘p"‘ 4 rs 1- 1 . P . J r\ r r*' x 7- I“ x‘ 1 F“ D -
ceivaoly be acconplishco in an iniiVicual case, the measuring 01 tle

On 1 1 f1- ‘ ‘ ' 1\ '7’ ‘ ‘ .P “34‘1" : ‘1’\ : r‘
eiiect of coca factor woule prooaely so 01 .itole use in ct er situa—

tions. Preliminary evidence ineic tcs that the factors resuoi ble
for the decrease in man—hours as the quantity of output LS iicrezsed
Ray be Jouped un Li er the folloxing catt orics (l): Jn70"er attrilutes,

including learning on the part of the orxanisation in the e rly sta gas

L)

of the prOg ram , morale, employee su.; estion Lsystem, aid 'nfluence of

[I '1

incentives. (2) Engineering eiior ts, including nore effective com—

UIJCation, clarification of drawings, clininatio of errors, and

9

simplification of deSign. Industrial engineering activities

‘3
U , . . n .
It should be noted that at no tire durinv the production Oi Six
thousand 3—17 bombers at :oeing d:d the curve cease to decrease.
Tnere is no proof at this time, whether the time reduction curve will

1

become horizontal as output is con inflec-

2'm u 2"” ', h n p 1,nfl o d an :. ' bra new +° a
QllCCt searlnb n tlJC ani netnoos. (J) bryaHLCSthD an} e lectiv —

0 x .1 I. L' ». w° -cn tr“ at man is
ness oi tne procuction czo it rcol fuzicti 01 Jill Ci ect tau vycrbm e .n

'1: " ,. (”,1 ‘ . H,L,\ J. ,4.
i an, add tgu OJosfis 0; She?—

4.“ .M -1,-_.,.
LOL. n; eooruinat

_J.

i316). (1;) Tile tJroe oi;

. ,L g,- i 21,. ., ' .0 _, A , ° .i l “1-..,5'1 ..
mated macnlne tools has an inlluer ce on nan—houi reuuiie»enos. umvaQj-

ment of a more efficient materials nana;enent SJstem will also tenu to
9
decrease costs. “agile it is certain t: at some learrirg on the part

the workers accounts for the sizeatls decrease in tine at tie

n " LON/v H n - 1 -. a -‘ . pm ‘ 1“, J- ‘.— 'r w 1 .
e rlJ SLNLCQ of a nron action 0100 a“ it seens clear tgdb neJoie tnis

initial stage the eureen of cortinued decreases must he on nanagenent.

‘
v

I
A

It is necessarv that Iona»3n,nt or roviJe t

(D
._J
)
C‘s
(r
w
0)
:3
r.4.

’0
(2‘
:3
o.
(+-
p..-
t
(L)
U)
('7-
{a
C:
H
L
(0

n 1W . H“ ' - (-1—- .\fi‘ ‘\ 5 f. n 439/ L: l— , r . ‘,~. .\ \ P - .‘
to iurtner ILQFUVGACflt. The 3_ooztanee Ol einectiVu org ni at on dLu

 

, -3‘ o ,1 .,-mi .vflJ. r 4. .fi—LJ.
COOFulI.ati on 0; all d‘gartuerts Carnot ‘e OVHW<rJug ”net.
" f‘ 1 f‘ ' ‘ ° N
so 0, tne ‘izo “e”:et1on curve
"11 4' I ‘I‘u‘ 1 ’V -. . -" w -r ', J’ r~ ‘ ~ r ‘1‘ r ‘1!“ ‘7‘ . - ~I‘ ‘ r‘ 1-
;Qe b1. Le I‘GCliCtlQ-W CLATVC LL13 Jul, to LIL-JG LU t '8 «'3 l1"): c:_.: t 111.1 ll; cl“;
A
if ",L Q,‘\,') 1\" n I t. n "L "“V " .\ c—r‘J' .. - ‘x‘ r J
.Lll la oe lp‘j”) , NIL-1‘. {fit—103 {UFOQUC L, LON O; o; 1.. __1.CI‘ C 4 Y‘C‘I‘m! t 434'“ Li2;:f‘-171‘”.D;.‘,’.
U

' i ‘ a

1; t' 'nn. r ;.. ~\1 L . ..,- . ,.Lw. i
Ab this st1Qe, the tire resuction curve se-vei primuiil; ~s a tool of

P , f ,— F‘ ‘ '5 -. _ v _- ‘_ 1"” _° " ° 1 '

lorecaetin. llou tin: -“1 k3 reasonaole tr pygoc+ 3;3ng *sgn
T':‘.(“ r. 7" “"J- .x . . , '- 1, *. —'- r -r , -r r . r r~ {‘J- —\, '_ _ L , ~ 1‘ _ > “
“Mo 2...; C..cl"CILC UT‘UQNCJ c0 ‘UL,’ L, 93 {would wilful“ ‘l CULKJIQ bgl 1;.) .) \LJH.‘ ’1‘;

tan b 'J- ~- 1°.“ ' n -.: "4.. ...
~H u OILClt llluLC. Also, 94'.,LL)LJ.LH‘J

xi
T“ . s . ’5 fl “
,, n , 1+F‘ Yur,‘ (. in L .' a "pn‘ .
:or a more netaileu a; cus ion oi actors “hie; a. set tL‘“
. J n}.
reouc1lon owe oncouer 7.

- 7 ‘l‘ ‘ ‘ -»< T" ~v- j I Tnl'yr x? 4 '0‘“- ‘n \~“—1 ‘ H . ’7
u. u. nlune ans 1. a. Olris, "nirove “Dal ”J, (e31u“,ho oLlJ
“Ortw-l 33.793"; Cfi‘fl I‘Ij—h‘t. A (‘1 Y“ "I

A - ti; 4 ,_ Q- [1. (.1 1011,10 L... , :1. IV.

e interval Getween tne e rs

Flow time uaJ oe (it cfinei as th 1 s
,
r expez;1uc ed in the manufacture 0

UFO auuction tour and the last hou
proauct.

Furl“

_ 7-
inadequate or in short supply. hilitary agencies,whicn were charged
with the procurement responsibility had to keep close score on nan-
power, facility, and materials utilization. As a result, the Army
Air Forces, Air Materiel Command be¢an a nandatory production data
reporting system which would enable it to control production to a
greater extentlz.

By the end of the war hundreds of aircraft producing facilities
made use of the time reduction curve technique. Ihen aircraft pro-
duction declined at war's end, there seemed to be also a decline of
interest in the time reduction curve, except for the large airframe
manufacturers, who continued to apply it to an ever greater variety
of problems. The post-war period has witnessed the introduction and
application of the time reduction curve technique to civilian produc-
tion. The beginning was made by the civilian subsidiaries of the
airframe companies.

The Bureau of Labor Statistics has examined nan-hour cost data
of a number of ship manufacturers. It is reported that there was an
average decline of sixteen to twenty—two per cent in the man-hours
required as the quantity produced doubledlB. Professor Lryan in a
study of a shoe manufacturing situation found that direct man—hour
cost per unit declines even after cumulative production of a pair of

12 - ., ~ a . i .. - ,
Source Book of horld Jar_ll DaSlC Data; Airfrafle industgx,
V01. 1, A. A. F. Materiel Command, Hright Field, Dayton, Chio, (n. d.)

 

13 F. J. Montgomery, "Increased Productivity in the Construction
§g4Liberty Vessels", Monthly Labor Revieg, (November, 1943), pp. 861-

 

C)
.4)-

boots has passed the ten thousand mark. Recently it is reported

that the time reduction curve applies also to the production of machine

tools,15 and electronics. Andress states that the time reduction

curve "Holds true whether the industr' is aircraft metal workin ,
9 9

textile or candy making. What was not known until a decade ago is

that the rate of improvement is regular enough to be predictable. It

is this fact that makes what would otherwise be a rather common—place
observation the clue to a broader and more practicable concept for
business."

Today the time reduction curve is used as a tool to provide the
solution to many manufacturing management problems, not only in the
aircraft industry, but in a number of other industries as well. An
indication of the importance of the time reduction curve to industry
may be inferred from the following facts:

(1) hanufacturers use the curve to estimate the cost of defense

contracts, which are then negotiated with the Air Force.

(2) The Air hateriel Command uses the curve to establish the

mobilization potential of production facilities.

(3) The Air hateriel Command uses the curve to appraise contrac-

tors' performance efficiency and to check the progress of

14
Stanley E. Bryan, ”Value and the Learning Curve," Purchasing,
(September, 1954).

 

l , .
59. Z. Eirsch, ”Landfacturing Progress Functions," The Review

EilEconomics and Statistics, Vol. 34, (Ray, 1952), pp. le—lhfi.

lédeno H. Cole, "Increasing Utilization of the Cost—Quantity
Relationship in hanufacturing," The Journal of Industrial Engineering,
(LéyAJune, 1953), pp. 173-177-
lafrank J. Andress, "The Learning Curve as a Production Tool,"
‘Eérvard.Business Review, (January-February, 1954), p. 87.

\g)

current contracts, as well as production dependability.
anufacturers use the curve ll

‘
f“ ‘r w‘
onlC 1..

(4) The Air hateriel Command
eating the feasibility of

planning, predicting, and t

schzdules.

(5) [anufacturers use the curve to develop man—hour requirements

for specific production programs.

(6) The fir Force uses the curve in negotiating prices of de—
fense material. The prime contractors are using the curve
to price subcontractor furnished materials and parts. In
other cases, where prices are negotiated, there is a ten—

dency to use the curve to arrive at a realistic price.

(7) hanufacturers use the curve to determine floor space re-

quirements, assum’ng that a standard average number of

square feet of Space are required per wormer.
(3) Using this technique it is also possible to determine the

assembly tool requirements.
(9) The curve is employed in computing the working capital

required during the manufacturing period because, t
of greatest financial drain is at the beginning of a pro—
gram. The cost of producing the early units of a new

product exceed the reven es.
The above list of uses is by no means complete. Cost control,
for example, is another area where the time reduction curve may be
USed. It does not appear that possibilities for additional applications

-10-

have been exhausted.

Purpose of the Study
The time reduction curve is one of the instruments which is used

3

cy the U.o. Air Force and the airframe industry in forecasting produc—

tion requirements. Recently it has found increasing acceptance in

other industries.
The purpose of this study is to determine the reliability of the

time reduction curve as a tool of forecasting irect man-hours in

certain manufacturing situations. For the purpose of this study, the

time reduction curve is defined as the relationship in which the cumu-
lative average direct man-hours per unit used in the manufacture of a

product tend to decline by a constant percentage as the cumulative

quantity produced is doubled. Where this relationship is present, it

may be represented by a straight line on double logarithmic scales.
The following questions relative to the time reduction curve will

be investigated: First, does the time reduction curve phenomenon exist

in manufacturing situations other than those where production activities

are based on a planned time reduction function? No assumptions are

made relative to the effect that such use of a preconceived time reduc—

tion model will have on observed man—hour data. However, it appears

18.
The following publications contain discuSSion of the uses of
R. Brenneck, ”The Learning Curve for Labor

the time reduction curve:
nears — for Pricing," 3AA Bulletin, (June, 1953), pp. 77-78; molfe

Myer, industrial Accounting with the Learning Curve,” The California
gcrtifiod Public Accountant, Vol. 33. Ho. 3, (February. 1956). pp. 35-
Q4; E. J. Blame, and Jonald Peitzke, Purchasing with the Learning Curve,
dorth American Aviation, Columbus, Ohio, (August, 19535; V. F. Brown,
vement Curve, Boeing Airplane Company, (Wichita, Kansas,

HT

LA

(Larch, 1955);

(\
Reno 2. Cole, "Increasing Utilization and the Cost-1uantity
The Journal of Industrial Engineering,

The Imoro

delationship in Eanufacturing,"
(naszune, 1958), pp. 173-177.

-11-
desirable to analyze empirical data observed in situations where the
curve is not used in planning and controlling production requirements.

Second, what is the reliability of the linear function of the
time reduction curve on log-log scale? What are the reasons for devia-
tions from a straight line on double logarithmic scale?

Third, what is the magnitude of variation in the rate of time
reduction among firms manufacturing similar products, non-similar
products manufactured by one firm, and also various models of a basic
product type manufactured by one firm?

Fourth, if the variation in the previously experienced rate of
time reduction is large, is it possible to estimate the applicable
rate on the basis of man-hour data experienced in the manufacture of
an initial quantity of units?

Fifth, in view of the findings relative to the above questions,
does the time reduction curve have value in forecasting direct man-
hour requirements?

This study is concerned only with the direct portion of the man—
hours expended and chargeable to a specific product. Where this rule
is violated, a note to this effect will be included. Because a change
in characteristics of a product usually affects the man—hours required,
accurate forecasting necessitates adjustment for the change in order
that a comparable basis be maintained. Accordingly, a method of time
reduction curve adjustment for design changes will be proposed.
Finally, certain relevant problems will be indicated for future invest-

igations to develop better man—hour forecasting techniques.

-12-

host of the empirical data used in this study were obtained
directly from three mid—western manufacturers through extensive per-
sonal visits to the man—hour generating, as well as all other departments
concerned with man-hour data accumulation. Because of the time, scope,
and otherlimitations it was necessary to confine this investigation to
three manufacturers, and some data gathered by the Air Force.

Chapter 2 contains a review of the historical development of the
time reduction curve, as well as a summary of the more important contri-
butions to the curve literature. Chapter 3 contains an analysis of
the time reduction curve theory, assumptions, and variations. In Chapter
4, historical man-hour data is presented. Chapters 5 and 6 are devoted
to analysis of data with specific reference to the above hypotheses.
Factors which are judged to have an effect on time reduction slope are
discussed in Chapter 7. Hethods of adjustment for changes in the
product unit are considered in Chapter 8. Summary of conclusions may

be found in Chapter 9.

CHAPTER II
HISTORY AVD DEVELOPKEHT
THE TIEE RE%%CTION CURVE

Introduction

Kany have described learning as the source of all human progress
and improvement. Whether or not the above statement is accepted,
there is little doubt that learning in its broadest meaning has been
responsible, to a large extent, for the relatively high standard of
living enjoyed by Americans. The short—term and the long-term
success of every manufacturing enterprise depends on continuous
improvement of its service to society. One aspect of this improve—
ment is that the cost which is required to produce the products
demanded be reduced in terms of effort expended on their acquisition.

THE INDIVIDUAL LEARNER'S CURVE

The fact that as an individual repeats a physical task his
performance improves has been known for a long time.1 It is probably
this fact more than anything else that is responsible for the (early)
mistaken notion that the time reduction curve phenomenon is attribu—
ted to learning on the part of the individual, in its entirety. The
time reduction curve was originally known as the learning curve, and
the latter term is still being used by some companies, although the

misnomer is quite apparent from the fact that the term learning curve

Ralph C. Davis, Industrial Organization and hanagement, (Yew
York: Harper and Brothers, 1940), p. 338.

-13-

-1M-
2

has been used by psychologists for many decades. This is not to
argue that an individual worker's learning, through repetition or
otherwise, is not reflected in the time reduction curve. On the
contrary, evidence seems to indicate that the high rate of improve—
ment at the early stage of a program is in large part due to workers'
learning. The inadequacy of the explanation of the time reduction
curve in terms of workers' learning alone becomes quite apparent when
the time reduction curve continued to register decreases in man—hours
even after thousands of units were produced over an extended period
of time.

Industrial psychologists generally agree that as a worker repeats
a manual task, the time required to perform this task will decline.
This may be illustrated by a learner's curve. Figure 2.1, relates

productivity to the number of weeks the employee is on the job

Plotting the number of units produced per day on the vertical axis

and the time in days on the horizontal, results in a typical learner's
curve. The normal shape for this curve is a rapid rise at first, then
less rapid until it flattens out. At this point, the learner has
reached what is often called standard or a 100 per—cent normal

LF
0 ’ ° vr w ‘ " ‘
elfiCiency. nadley proposes that this curve be used to estimate

the required training time for new employees, and also computing

ZDonald A. Laird, and Eleanor C. Laird, Practical Dusiness
Vy 1 f,‘ " ’ ‘q.’ "' fl , r’
EEJCflOloaf, (iew York: thraw—hill :ook Company, 1936), p. 376.

 

Ibid
*-

9 P0 377.

F Franklin C. Koore, Production Control, (New York: YcGraw—Vill
“00k Company, 1953), Chapter 9.

 

~

Per Cent of hfficiency

FIGURE 2.1

A TYPICAL LEARNERS CURVE

 

 

\

 

 

 

1 5 10 15 20
Weeks On The Job

Source: Hypothetical Data

-16-
learners' allowances. It may be stated that the learning period is
a function of the complexity of a given task. Some tasks require
little time and ability to master while others take a relatively
long time. Psychologists agree that ability, incentive, and attitude
are some other variables that enter into a learning situation.

The discovery of learning curves has been attributed to Dr.
William L. Bryan. His studies of telegraph code learning were a
most significant contribution to applied psychology, and were publis-
hed first in 1397, at the psychological laboratory, which he started
nine years earlier at the University of Indiana. Bryan was the first
to find that learning does not progress smoothly, that learning is
most rapid at the beginning, then it slows down as the ultimate in
skillis approached; and that there is a plateau in the learning
curve, a time when the learner does not seem to improve, and the
curve may actually turn downward.

Since this pioneering effort on the part of Bryan, many indus—
trial psychologists have studied the learning curve for different
industrial situations.8 Regardless of the task involved, a clear
similarity in the learning curve is in existence. Tiffin reports

5

J. R. Hadley, ”Learning Curves on Log-Log Paper; Technique

for Determining Learners Allowances," Advanced hanggement, (April,
1950), pp. 16-17.

Dr. Bryan later became president of the University and held
that post for 35 years.

W} L. Bryan, and N. Hartern, "Studies in the Telegraphic
Language," Psychological Review, (1899, Vol. 6), pp. 346-376.

9
“ Uliilton L. Blum, Industrial Psychology and its Social Foundations,
(New York: Harper and Brothers, 1956), p. 213. ——

-17-

learning curve of "normal" shape, i.e. sixilar to that des ribed

in aoove pa wr g mphs, has been found to exist in hosiery pr:duction.9

A study to determine the shape of learning curves for industrial

motor tasks is one of the most recent contr ' butions to learning curve
10

knowledge. In this mudy learning curves were obtained for persons

on twelve diiferent sewing tasks. The e tasks rang ed in length of

learning time from seven to twenty—seven weeks for individual learners.

There was considerable variation in job characteristics ranging from

simple automatic tasks to those requiring a good deal of adjustment

in behavior. All jobs observed were on a si il:r wa e incent :_ve

S
syste:n, and in all cases output was not counted until at least one

satisfactory unit was produced. Iot only were all the average learn—

,
z “;A

ing curves similar, but when they were equated for different learning

hp

times, and the d m; went levels of potential efficiency, they appro—
ximated closely the identical shape throu hout the perioc. The rate
of change was similar and comparable for the different tasks, and

therefore, it was possible to determine a typical curve for learners

in this particular situation.

Ind ustiral psycholo; ists agree that two changes take place

when a worker learns on the job. The first category of changes
may be called qualitative changes. These include all the improve—

ments that the individual acquires in his behavior either consciously

Joseph Tiffin, Industrial Psychology, (Yew York: Prentice—
Hall, Inc., 1952), p. 173.
10T , _, i . . , fl.
u. C. Taylor, ”an investigation of the anape of Learning
Curves for Industria i Rotor Tasks,‘1 (Unpublished Iaste r‘s Tiesis,
Cornell U.iversity,l 1951), p. 160.

;I__J

FIGURE 2.2

Two INDUSTRIAL LEARNING CURVES

1A0.

120 l

100

 

 

 

 

 

80 ‘ ..o.. '

 

6O

 

 

1 PRODUCTIVITY

hO

 

20

 

 

 

 

 

 

 

 

! ' 5 —£ 66 ‘730 100

Days On The Job

Source:

 

i Taylor;J. Cw, "An Investigation of the Shape of
1 Learning Curves For Industrial Motor Tasks"
unplublished Master's thesis, Cornell University,

1951

 

-19-
or unconsciously, and consists primarily of modifications of the form
of movements as the task is repeated. A study by de Kontpelier of
France, attempted to determine movement pattern changes as the cycle
was repeated. The motions of the subjects were recorded photograph—
ically for each cycle. A steady increase in speed was observed
throughout the thousand trials. There was also a clear improvement
in the form of movements. The most important change was the elimina—
tion of most corners and angles.11
In addition to analysis and research of qualitative changes,
psychologists have studied the factors influencing the shape and
the length of individual learning curves for various tasks. From
the management point of View, the individual learning curve is of
interest for a number of reasons. First, learning curves are valuable
in diagnosing problems of learning, indicating difficulties and
reasons for delays in learning by the individuals and groups. Hext,
learning curves may be used in evaluating methods of teaching and
other changes in working conditions and methods. Finally, they give
the individual learner an immediate goal to work toward. In one
situation the workers are told what the reasonable rate of progress

should be, so that the worker will not be unduly discouraged.12

llT. A. Ryan, and D. C. Smith, Principles of Industrial Psychology,

(New York: Ronald Press Company, 19545, p. 43l7_
lzfielrose Hosiery Company, reported in Joseph Tiffin, Industrial
Psychology, (New York: Prentice—Hall, Inc., 1952), p. 310.

 

-20-

In some cases the workers' motivation can be kept up by tying
a wage incentive plan to the learning curve, given the learning curve
for his job.13

The existing evidence is virtually in agreement that there is
a horizontal level which the learner reaches after a specified time
on the job. The agreement is far from unanimous. Slum states that:

Too often the concept plateau appears in connection

with the learning curve. This is an overstated and over-

worked idea. Sometimes there is a flatness in the learn-

ing curve which is eventually followed by a spurt. This

flattening indicates a period of no apparent progress and

is referred to as a plateau. There are many reasons for

the appearance of a plateau in the learning process. It

may be the result of lack of motivation, inefficient methods,

or, very often, ineffective teaching and poor training.

However, a plateau is not an integral part of the learning

process; hence one should not be concerned by its absence.
Blum argues that learning and productivity should continue to increase
indefinitely. If so, the possibility of existence of a continuous
time reduction curve which is solely due to learning is obvious.
Another authority states that the plateau is peculiar to industrial
situation learning, and that a plateau need not be a permanent pos—
ition, and that it is possible to prOgress from there to a new

1

plateau. 5 The possibility of this happening has been demonstrated
in many cases where a new method or motion is discovered and adopted
by employees, presuming that they had incentive to do so. As a

practical matter there is, in most plants, a standard level of perfor-

mance, which when reached by an employee, satisfies supervision.

 

13.1. R. Hadley, 93. cit., p. 16.

. Hilton L. Blum, Industrial Psychology and Its Social Founda—
tions, (flew York: Harper and Brothers, 1950), p. 450.

 

5Ryan and Smith, 93. cit., p. 438.

 

-LKI-

Furthermore, any additional progress is probably discouraged by the
union, thus learning or improvement may be absorbed by the worker
through certain well developed techniques. Ryan and Smith attribute
plateaus in learning as being primarily due to changes in motivation
of the learner.16 Another important reason given by the above authors
is that level periods exist because the workers practice incorrect
responses, which are not conducive to improvement.

When there is a change in method there appears to be what might
be called a plateau. Actually, it is the end of a learning curve
for the old method and the beginning of a new learning curve for the
new method. In some industrial learning situations the learning of
new methods cannot be undertaken until the previous method has been
mastered. There are some practical implications of individual learn-
ing curves. Taylor reports that many of the learners have quit their
jobs while they were on a learning plateau. Careful observation
showed that the experienced workers were using a different method,
which unfortunately for the learners, was not easily mastered.l7

we have seen that authorities are not in agreement as to the
shape of the learners' curve. host of the writers, whose work was
reviewed, appear to be in favor of the more popular hypothesis that
after a certain period of time there is a tendency for output, as a
result of learning, to reach a plateau. A break—through is probably

possible providing the worker has sufficient incentive and perhaps

 

16Ibid, p. Ml

17Taylor, _2. cit., p. 23-

-22-

some help in mastering a better method. Thus, we may condlude that
after a certain standard proficiency is reached, no significant
progress should be expected without the efforts of management. 18
Performance must level off at some point, because of workers' limited
ability, even if other limitations do not exist.

we have discussed the industrial psychologist's views on the
shape of an industrial learners' curve. It is evident that there is
a definite relationship between the learning curve as discovered by
William Bryan, and the time reduction curve which is the subject of
this study. The basic difference seems to be in that the former is
concerned with a production unit consisting of a sin le individual,
whereas the latter is concerned with the progress of a productive
organization which may consist of many thousands of individuals.

T_.D;FTLPY31TOF'TW‘TDIB
REDU ”‘IIC. ’ CURVE THEORY

In deciding whether or not to review an author's work in the
following pages, the criteria of contribution to theoretical or em—
pirical knowledy e of the time reduction curve was used. First, the
two main approaches to the time reduction curve theory will be dis-
cussed; next follows a chronological review of what appeared to be
work which contained original material at the date of publication.
The Orthodox Formulations of the Time Reduction Curve Thquy

The original formulation of the time reduction curve theory is
attributed to T. P. wright. However, two authorities believe that
Leslie McDill should get the credit for the original formulation.

3

'Depending of course on the effectiveness of incentives and
the imagination of the individual worker, there will be exceptions.

 

-23-
Thus, Reguero states that:
Credit for the original investigation of
airframe production data which led to the for—

mulation of the learning curve theory is given
to Leslie KcDill, who was commanding officer at

f

KcCook Field19 in 1925.30
Another writer who attributed the theory to thill, is Hax Stupar
who says:

.About 1932, Leslie McDill, studied costs

of airplanes in various quantities and arrived

at the conclusion that doubling of the quantity

resulted in an average man—hour consumption of

80 per-cent of the original value.2
Neither of the two authors give the source of their information.

The subject of cost of airplanes was of interest in the middle twen-
ties in connection with discussions of economical mass production of
airplanes for private use. It is this subject that led T. P. Wright
to publish the article to which the origination of the time reduct—
ion curve theory is attributed.22

Whether or not Wright originated the time reduction curve can-

not be stated with certainty. Since thill did not publish his

findings, we will probably never know exactly what his contribution

is. we do know that wright was the first to make the theory known.

 

19lCcCook Field was the predecessor of Wright-Patterson Air Force
Base, near Dayton, Ohio.

20K. A. Reguero, ”An Economic Study of the Airframe Industry,"
(Unpublished Ph.D. dissertation, Department of Economics, flew York
University, October, 1957), p. 213.

21 . , . . .

Kax Stupar, "Forecasting of A1rp1ane Lan_dours," Unpublished

manuscript, Headquarters Air hateriel Command, (1942), p. 7.

22T. P. Wright, ”Factors Affecting the Cost of Airplanes,"
Journal of Aeronautical Sciences, (February, 1936), pp. 122-123.

 

 

 

 

 

 

 

I"

 

 

 

 

 

 

 

 

 

 

 

- . .
-... --.¢-..._ 1--.: ..o-.«....o.,v-. ....-9.--..
. .
o . .
n . .
. .
younl v-5. .v.t-oto1vo..-.....n-+.aou v.:.4.,.u
.. . .
o . ..
. . s
v o hr
IIIOII"- "-.9Il§n'| 4
. .n . .....v t o. o .... .. . .u..
...o . . ..-.
#0. O‘!“.‘ IIO|0+

 

 

"G'IVIIII'IA‘I,

:Ill'lllulll

Eli'l'r'

 

 

 

— (5. J -
To quote wright on the time of his work:
The present writer started his studies of the

variation of cost with quantity in 1922. A curve

depicting such variation was worked up empirically

from two or three points which previous production

experience of the same model in differing quantities

made possible. Through the succeeding years, this

original curve, which at first showed the variation

in labor only, was used for estimating purposes and

was corrected as more data became available.23

According to'Uright, the most important determinants of aircraft
production cost are design factors, tooling, engineering changes,
size and quantity produced. The design factors include the type of
construction material costs, simplicity of design, and reduction of
parts. The tooling factor of production cost depends on the quantity
produced and on the susceptibility of the design type to be produced
on available tooling. Changes require many expenditures be51oes the
direct cost of incorporating them, e.g. shop delays, are another item
of costs. Size of product has the effect of favoring decreased costs
because the number of parts does not increase at the same rate as
size increases. Also, in a large airplane, the parts need not be in
miniature size and gauge, and therefore, are easier to handle.

It is the effect of quantity on production cost that was of

greatest interest to wright, and the one area where his contribution

has been the most fruitful. ‘Wright holds that the three major costs
Of production vary with the cumulative quantity of production. It

may be noted here that although it has been a widely acknowledged

fact that labor and overhead vary as the quantity of unit produced

 

23Ibid, p. 122.

is increased, there has been a surprising lack of development on the
direct material curve which wright has originally suggested.

wright attributed the reduction of labor time as production
quantity is increased to four factors: (1) The improvement in pro—
ficiency of a workman. (2) The greater spread of machine and fixture
set up time in large quantity production. (3) The economy in labor
which greater tooling can give as the quantity increases. And finally,
(4) as more and more tooling and standardization of procedure is intro-
duced, it is possible to use less skilled labor.2

In his analysis of empirical data, wright found that the function
between cumulative average direct man—hours and cumulative number of
airframes produced could be represented by the following function:

Y = axb (2.1)
Where:

Y is the direct average man-hours

x is the cumulative output

a is the parameter which indicates the direct man—hour cost for
unit number one

b is the second parameter which defines the slope of the time
reduction curve.‘

5 is the slope

 

24Ibid, p. 124.

25In time reduction curve terminology, slope is defined as the
ratio of the unit (or average) man-hour cost at two pOints of pro—
duction. This differs from the mathematical definition of slope, f
where the slope of a function is defined as the first derivative 0
the function.

 

my",

/
~14! —

For the empirical data available to him, Wright found that "b" has a
value of - .322 an 80 per—cent slope is obtained by substituting

- .322 for "b” in the following equation:

S = a 2x b
ax (2-2)
or
log S = - .322 log 2 (2.3)
or
S = .8 (2.1»)

The above illustrates the customary practice in time reduction
curve work of obtaining the slope at double the present cumulative
output, or in other words, quantities that vary by a factor of two.
When it is assumed that the cumulative average man—hours are related
to cumulative output as shown in equation (2.1), the resulting cumul—
ative total curve will be:

Y = axl+b (2.5)
and the unit curve will be:

Y = a(l+b)xb (2.6)

There is some question as to whether Wright meant equation (2.1)
to describe the unit curve or the cumulative average curve. The con—
troversy should be settled by the following passage in Wright's
article:

A curve may be plotted which shows directly the
relationship between the two variables and when plot—

ted on log—log paper, it becomes a straight line. nIn

Figure 2.3 such a curve appears; there called the do

Per-cent curve which is represented by a value of .322

for the exponent x (Y in this study) in the above for—
mula. This 80 per-cent has a definite meaning in that

 

Afl
-1“)-

it represents the factor by which the average labor

cost in any quantity shall be multiplied in order to

determine the average labor cost for a quantity of

twice that number of airplanes.20
Wright was talking about cumulative total output and cumulative aver-
age man-hours per unit.

‘Ue have already mentioned above that Tright hypothesized that
material also decreases as the quantity increases. He found, for
instance, that the amount of usage for the first five units alone
amounted to UO per—cent of the cost of purchased material. "It
reduces rapidly as quantity increases, to 25 or 30 per—cent in quantities
of twenty-five to fifty units and down to 20 per-cent in a quantity of
1 1 ° 0'27
one hundred units.-

In addition to the reduction of waste,'flright maintains that
greater cutting efficiency and more economical purchasing partially
explain the reduction in material cost. Other possible factors at
work are reductions in price of materials because of quantity purchases
and greater vendor efficiency. Empirical data available to Wright

. . I
showed that a raw material cost improvement curve of 95 per—cent anc
purchased material curve of 93 per—cent, were realized. Tne aoility

to obtain a steeper curve in the case of purchased material is explain—

- - - a + _
ed as being due to a greater proportion of labor in the lauter.

 

 

 

 

James R. Crawford

Crawford is one of the most prolific contributors to the pub-
lished material on the time reduction curve. Unfortunately, most of
the material developed by this author has been in the form of company
manuals which are not available at this time. His chief contribution
to the time reduction curve theory was a study of two hundred jobs in
the airframe production process, which resulted in a new formulation
of the time reduction curve. Crawford shows that the relationship
between direct man—hours per unit and the cumulative unit number could
be described by the function Y = axb.28

The above equation is identical to that developed by Wright,
except that in this case it is assumed to hold for the unit curve,
whereas Wright used it in connection with the cumulative average curve.
A number of Crawford's attempts to develop a time reduction curve of
simpler equations and formulae did not yield forms that were adopted
either by the industry or the Air Force.29

Crawford's most recent contribution are Improvement Curve tables
which give values for a set of straight lines on logarithmic scales.30

Learning on the part of the individual worker is held to be most

important by Crawford. He also emphasizes that learning does not mean

 

20J. R. Crawford, Learning Curve, Ship Curve, Ratios, Related
2333, (Burbank, California: Lockheed Aircraft Corporation, n.d.), p. 52.

29J. R. Crawford, Estimating, Budgetipg, and Scheduligg
California: Lockheed Aircraft Corporation, 1945), p. 51-

 

, (Burbank,

3OJ. R. Crawford, “Learning Curves," (Unpublished manuscript,
1958), p. 20

 

«\x

-30-
faster motions, "but the improvement in approach which enables him to
eliminate lost motion with no additional effort and oftentimes with
31.. ,. . .

less effort." rurther, he states tnat jobs which require the most
mental effort improve at the most rapid rate. The mental effort may
be due either to complexity of the work or lack of experience of the
worker.

Another work by Crawford that is worthy of our attention here, is
an article which deals primarily with statistical data requirements of
a system of production control, however, there are some direct references
to the time reduction curve. The author makes the following remark in
speaking of determinants of the time reduction curve:

The rate of decline of a progress curve is

determined by the amount of knowledge the employees -

including the service organization - have to gain

concerning a particular model. Thisis found to

correlate with the amount of residual experience in

the plant at the time the project is started. This

experience may be in the form of trained personnel

or immediate experience with a previous model. From

these two elements, the whole series of man-hours per

unit can be determined. A simple follow—up by means

of manufacturing accounting records, enables pgrform—

ance to be measured within very close limits.

Unfortunately, Crawford does not go into detail as to how knowledge

that the employees have at a particular moment may be measured, and

levels of performance on a new program predicted.

 

31'J. R. Crawford, Estimating, Budgeting and Scheduling, (2urcank,
. ° 1 -~ A - \ A)
California: Lockheed Aircraft corporation, l9h5), p. 2+.

32
Ibid, p. 26.

33J. R. Crawford, "Statistical Accounting Procedures In Aircraft
Production," Aero Digest, (Karch 15, 1944), pp. 1-8.

 

-31-
OTHER COXTRIBUTIOTS

A. B. Eerghell

An excellent mathematical treatment of the time reduction curve

may be found in Berghell's book entitled Production Engineering in the

Aircraft Industr‘ which contains a chapter on "Learning Curves."
i, L :3

Those who prefer the exactness of mathematics should find the chapter

interesting.
I. I. Laddon

Laddon was Executive Vice-President of Consolidated Vultee Air—

craft Corporation. The article he presents is of interest because it

contains a description of change in the production function as the

total quantity to be produced by a company is increased. The company

was engaged in the manufacture of the "B—ZM Liberator" bombers.

Despite a tremendous labor turnover due to selective
service demands, plus the complication of hiring and train-
ing thousands of unskilled women, the company today is pro—
ducing 2.5 planes for every one produced in April, 1942,
while employment of production workers has increased by
10 per-cent. Employment of women has risen from less than
1 per—cent in December, l9kl, to more than 43 per—cent at
this writing, a great majority of women being hired to
replace men going into the armed forces.

The author explains the difference in production methods that are

present when only sixty units are to be produced, and when an order

is placed for several thousand units. The company performed much

better than the customary 80 per—cent time reduction curve.

 

34A. B. Berghell, Production Engineering In The Aircraft Indus-
2219 (New York: KcGraw-Hill Book Company, 19hfi33 Chapter 12.
1"
3J1. h. Laddon, "Reduction of Han—Hours In Aircraft Production,"
8 ' - y,
aziaii22_. (nay, 1943), pp. 170-173.

-32-
Bureau of Labor_5tatistics Studies
The Productivity and Technological DevelOpment Division of The
Bureau of Labor Statistics, Department of Commerce has prepared a
number of studies of interest to a student of the time reduction curve.
hany studies were published by this agency on the decline in man—hour
requirements per unit of certain goods, unfortunately, this data is
not adjusted for major changes in the product unit, therefore, it is
not suitable for time reduction curve analysis, and will not be dis-
cussed here. A few other of these studies deal with time reduction
curve data, and their nature will be discussed at this time.
The Liberty Vessel Study
The first time reduction curve data on ship construction was
36
reported by Iontgomery in 1943. The study deals with the EC—Z
Liberty ship of 10,300 dead weight tons, which was designed for mass
construction. The statistical information for this study was obtain-
ed from the U. S. haritime Commission. The man—hour requirement data
represented both direct and indirect labor hours. The latter include
the time of supervisory personnel, technical, clerical, office, power
plant, and maintenance employees. The time of corporate officers,
auditors, general managers, and general foremen is included under in—
direct labor. The direct man—hours had to be estimated from actual
man—hours required for a group of ships, the total is then averaged

for the number of units within the group.

 

36F. J. Kontgomery, "Increased Productivity in the Construction

SguLiberty Vessels," honthly Labor Review, (Yovember, 19H3), pp. 861—
(-1 .

I\, "

_/‘)—

Between December 1941, when the first two ships were completed,
and April 1943, when nine hundred ships were delivered, the average
man-hours required per vessel decreased by more than one-half.
Nontgomery reports that the decline tends to be large at the beginning,
and that as production continues the decline continues but at a lower

rate, and states that:

It is probable that a similar trend would be

revealed by figures for a company making one auto—

mobile mpdel or some other item of complgé but

standardized equipment on a large scale.
Wartime Shipbuilding Stuqy

Another important study was done at the Bureau of Labor Statist-
ics by A. D. SearleBBand published in 1945. The study is similar to
that made by Montgomery (above) except that it covered Liberty, and
Victory ships, tankers and standard cargo vessels. Searle analyzed
data which was gathered by the U. S. Karitime Commission, the Havy
Department, and reports of shipyards to the Bureau of Labor Statistics.
The labor data used to determine labor requirements are total man-
hours defined in the same way as in the Hontgomery study above. The

data covers the period between December 1941 and December 1944 with

emphasis on the interval between April 1943 and December 1944. Searle

reports that:

Examination of the data for individual shipyards
showed that every time a yard doubled its output, man-
hour requirements per vessel tended to decline by a
constant percentage. The percentage decreases varied

 

37Ibid, p. 861.
Q
30A. D. Searle, "Productivity Changes in Selected'Wartime Ship

Building Programs," fionthlijabor Reviewi (Vol. 61, Ho. 6, December,
1945), pp. 1132-1147.

-)¢_

from yard to yard, but the average declines were almost 39
identical for the different types of vessels considered.

Searle found that the man—hour per ship data when plotted on log-
arithmic graph paper shows an 80 per—cent time reduction with each
doubling of cumulative quantity produced. It was found that within
each production program there was considerably more variation in the
rate of time reduction than between programs, however, in all cases
under consideration the percentage reduction in man—hours between
doubled quantities produced ranged from 10 to 26 per—cent. The study
concludes that differences in the types of vessel are less significant
in determining the rate of man-hour requirement reduction, than the
production function differences between individual yards. The above
two studies seem to indicate that the time reduction curve phenomenon
is present in ship construction programs.

'Wartime Productivity Chang,s in the Airframe Industny

This is the third in a series of studies which were made by the
Productivity and Technological Development Division Bureau of Labor
Statistics. This study was made by Kenneth A. liddleton and was
published in August of 1945, and deals primarily with productivity
changes. Kiddleton notes that there was approximately a tripling of
productivity per man—hour during the war and he attempts to explain
the factors which affect productivity. Among these, he gives the
greatest emphasis to increased total quantity of production and intro-
duction of mass production methods. In anticipation of labor short-
ages, the industry tended to hoard labor and as time went on the

39mm, p. 11144.

a A

companies tended to employ this labor witn greater efficiency. n3
these productivity depressing conditions were eliminated or reduced
during 1943,1he increase in output was remarkable. It is pointed
out that before the war there was very little specialization in the
airframe industry and as a result great versatility of labor was
necessary:
These mass production techniques, so largely

responsible for doubling airframe output per man—

hour between early 1942 and late 1943, are charac—

terized by specialization of labor, machines, and

hand tools. The division of production into re—

latively simple jobs would have been necessary to

allow rapid training of a great and large labor

force, if for no other reason.“0
Thus, hiddleton holds that the great increase in productivity and the
reduction of labor cost per unit is the result of technological changes
such as standardization of models, introduction of highly specialized
hand tools, and gauges. Kiddleton admits, that the introduction of
new methods and new production techniques, that is the rate of adopt-
ion of the new methods and techniques, depend largely on he nature
of existing situation and to some extent on the traditional methods
of the company. It is up to the management, in other words, to change
traditional methods.

In the preparation of this study Hiddleton examined individual
plant reports and compared the levels of labor requirements for

different kinds of planes. An attempt was made to construct an in-

dustry wide production index. This was accomplished by plotting on

 

40
K. A. Fiddleton, ”Wartime Productivity Changes in the Airframe

Industry," Konthly Labor Review,(Vol. 61, 30. 2, August, 1945), p. 220.

'1'?

 

 

‘1‘ o
IJONJ“.
fl:

 

 

 

 

 

 

 

 

A
vs
.’

-26-

the vertical axis the man-hours per pound of airframe and on the
horizontal axis the cumulative production pounds in the particular
facility. This method differs somewhat from the conventional method
where the units of a particular product are plotted on the horizontal
axis. hiddleton finds that the decrease in man—hours required per
pound is similar for all types of airplanes and therefore, this index
which uses the pound quantity as a basis provides a more useful index
for comparative purposes. The relative positions are very similar at
all points within the range of cumulative outputs for the different
plants producing various types of aircraft, although semewhat more
man—hours per pound were required for a one engine fighter than for
standard four engine bombers.

hiddleton a nits that it cannot be~assuned that airframe weight
is an entirely adequate tool in measuring productivity. For example,
it is found that more man-hours are required to produce a hundred
thousand pounds of combat planes than to produce a hundred thousand
pounds of non-combat planes such as trainers. In other words, a
hundred thousand pound production of a bomber should have more signifi—
cance in the index than a similar increase in the production of basic
trainers. Hevertheless, hiddleton argies that the average direct man—

hours cost per pound plotted against cumulative pounds produces a

F)
Q)
'3
(4'
CD

better indicator of the physical value of the work performed t3
number of units.

A general tendency for unit labor requirements to
decline by constant percentage every time a plant doubles
its cumulative production has often been noted. However,
it appears that earlier judgments of the rapidity of this

decline were unduly conservative. Some credence
had been given a standard 20 per—cent reduction
(an 80 per—cent curve) in unit labor requirements
with each successive doubling of output. The

present study indicates that a rate of about 30 I
per—cent would be a more representative average.

Ll
Thus, using the above indicator of productivity, Niddleton con—
cludes that it is the 70 per—cent time reduction curve that holds for
the aircraft industry during the last war instead of the normally
assumed 80 per-cent curve. Kiddleton found that a considerable varia—
tion does exist in the slope of the curve from one plane to another.
Whether this variation is of six

,5.
t.)

nificance, Liddleton does not elaborate.
However, a visual examination of hiddleton's chart Figure 2.h would
seem to indicate that the variation in slope is of some significance.
Daniel W. Carr

One of the writers who believes the time reduction curve should

'1‘!

take on the ”o- shape is D. N} Carr, wh at the time of his writing
:as associated with IcDonnel Aircraft Corporation. Carr does not
present any empirical evidence to substantiate his ”5" type curve.
However, he explains the concavity in this curve as follows: First

he assumes that each worker in quality production crews produces along
0 42 . ,. -

o0 per-cent curve. But Since the snifts and the crews are not hired
at the beginning of the program, but during the time of acceleration,
there is a different slope for each crew depending upon the tine that

it was hired. Thus, although the curve for the individual crew may be

linear function, the sun of the individual crew curves will be concave,

41
lbid, p. zZl
Q?
G. U} Carr, ”Peacetine Cost Estimating Requires Yew Learning

Curves,” Aviation, (Volume #5, April l9ué), 99- 76‘77'

k

-31)-
because the new crews are producing the first unit, while the first
crew may be producing their tenth unit. This condition produces the
concavity in the area "3", Figure 2.5. The steep segment between ”B“
and "C" according to Carr, is the result of technological improvements
in the production function, e.g. a greater improvement in tooling and
a break down of airplane into accessible production of sub—assemblies.
Quantity built is another factor which determines the steepness of the
curve between "B" and "C". The flat area is reached at "D" assuming
that no major changes in tooling or production techniques take place.
Thus, slopes, "A" and "D" may be used for projection of costs, but
".... is incorrect for budget or actual cost finding purposes. Beyond
b,
"D" costs slowly approach optimum."
Without redesign or additional tooling, there is

a definite limit below which operations cannot be per-

formed at reduced man-hours. On fabrication, this

limit is reached at any early stage, being governed

by the speed of machinery and not by individual skill.

In assembly accessibility may establish the minimum

hours possible with all operations a flat is reached

sooner or later beyondufihich only negligible improve—

ments may be expected.
Data on post war airframe production does not support Carr's "S"
shape curve.

The present study indicates that there is a high correlation of

man-hour data to a straight line.

43Ibid, p. 76.
44Ibid, p. 77.

Information obtained at Headquarters, Air Materiel Command,
Dayton, Ohio, (1959).

 

tan-hours

 

Flmfid.2.5

AN "53" 3mm: T171; r-gr.;)u3:'1< :1 Crown

 

 

_ B (Log-LO? Scale) I

 

 

 

1(0

10 Quantity
., . #3 3w, 4 . .' Y . ~ ‘0"
j.(\ur(je: Carr, G. “'5‘, 97} BBCOLVIHJ‘: {,C‘St F.f)t.i..<1t.xrtft Requires new Learning CUTIC.)
I‘xViilt Lon

Vol. LS, érril 19L5, r76

Time Reduction Curves in Great Britain

The first published evidence of time reduction curves existing in
Great Britain was indicated by Eric hensforth in an article published

'6
in the October 1947 issue of Aircraft Production. hensforth was
associated with the ministry of aircraft production in the second
World'War, and has gathered a considerable amount of material on air-
frame production in Great Britain. Of special interest to us is the
British experience with time reduction curves. hensforth found that
British experience was similar to that of American aircraft production.
British figures show the same general trend within rough limits of 75
per-cent to 85 per—cent.
It will be observed that when the same aircraft is
made at various factories the man—hours required do fall

fairly close to the cugves at the same relative period of
production development.7

Kensforth developed learning curves for various types of aircraft and
found that the slope varies, but all models under consideration fall
within 75 per-cent to 85 per-cent curve limits.40 Hensforth considers
the peak volume of production to be important in the reduction of man-
hours. He feels that required man—hours on relatively small scale pro-
duction are higher not because different methods are used, but because
when the scale of production is greater.it permits more specialization and

more rapid achievement of full dexterity. As an example, he mentions

a case of two factories in Great Britain which were producing the same

Eric Hensforth, "Airframe Production,” Aircraft Production,
(Volume 9, October, 1947), pp. 338-395.

Q7Ibid, p. 391.

48Ibid, p. 392.

 

 

 

-41-

aircraft with similar equipment and tooling. One factory was producing
about fifteen planes per week, and the other fifty-five per week. The
actual man—hours of the latter were half that of the former, and since
both of the factories were on a piece work basis, and the same rate
was paid, the earnings of the one producing fifty—five units per week
were two hundred per—cent higher. The difference in output per man—
hour of British and U. 5. workers is explained in terms of different
type of tooling employed in the U. S. The American plants used tool-
ing to a much greater extent than their Britisn counterparts.
The Hirsch Stuiy

Werner Hirsch attempted to apply the time reduction curve to pro—
duction of a large machine builder. 9 The author chose to analyze seven
machines, all of which were either new products or new models. Of the
nineteen time reduction curves fitted, only five had a correlation co-
efficient less than .35. The slepe of the time reduction curve varied
from 79.2 to 83.5 per—cent, depending on the type of machine that was
being manufactured. The average slope for the unit curve is 31.5 per-
cent. The average for the machining operations was 37 per—cent, and
for assembly operations 74.4 per—cent. Hirsch concludes that there is
very little relationship between direct labor requirement and scale of
production in the machining and assembling of a textile machine and
semi-automatic machine tool. He explains this in part as being due to
the fact that both machining and assembling in this situation require
relatively fixed combinations of labor and equipment. Although in
machining the setting up process is fixed regardless of the number of

#7 an,

'W. Z. Hirsch, hanufacturing Progress Functions," The Review
gigsconomics and Statistics, (Volume 3h, Fay, 1952), pp. lh3_lh5.

AJIIIII--——__.

 

 

-42-
units to be produced at one time, the labor savings or the decrease in
labor requirements were found to be very little after twenty lots of
five units each, is produced. The author describes this negative
labor requirement-cumulative output relation as being due to changes
in technical knowledge, which take place as cumulative output increases.
The following reasons are given for this decline in labor requirements:
(1) progress of direct labor, (2) progress of management, (3) progress
of the material suppliers. It is stated that the learning process of
the various groups in a firm is highly interrelated.
Because of this interdependence, management,

engineer, and direct labor must be in contact

through joint meetings, shop visits for engineer

and management, and a suggestion box. A similar

effort is needed to benefit from progress outside

of the firm.50
Hirsch also found that the height of the total direct labor reduction
function reappears with little regularity. This is so because the
height depends primarily on the complexity of the product. Hirsch
concludes that empirical estimates of time reduction function can be
used on the firm level as well as the national level for many purposes.5
Although it is too early to draw any general conclusions with regards
to the time reduction function in the machine building industry, it

seems that the empirical data gathered by Hirsch is an indication that

time reduction curve phenomenon exists in machine building.

 

50
Ibid, p. 147.

Sllbid, p. 153.

 

 

Reno Cole Survey

 

5’)
L,
This survey was done by Reno Cole the results of this are re—

produced in Table 2.1. Because 61 per-cent of the companies surveyed
reported that they do use the time reduction curve technique, it seems
that this technique has found a considerable acceptance in industries
other than airframe. It should be remembered, however, that this
survey took place in Southern California where the aircraft industry
is a dominant force and where other industries have had an opportunity
to adopt this technique from the aircraft companies. The survey was
restricted to non-airframe metal product manufacturing industries
having three hundred or more employees. As it turned out, however,
there is a large concentration of firms that supply the aircraft
industry and which do not qualify as an airframe compa.y, but which
nevertheless, work closely with defense industry and are in a position
where they have to work with the government and the large prime
contractors. Cole states that:
It is interesting that a high percentage of the

companies surveyed who reported use of the technique

considered it as a necessary part of planning. A

considerable percentage of replies were qualified,

however, by stating that judgment was required in

the use of the technique. This is, of course, true

of the application of any industrial technique, but

the reply would seem to indicate the absence of a

completely comfortable feeling on the part of many

who use the cost quantity concept. This undoubtedly

due to the limited amount of information available
for industries other than airframe.

 

52Reno 3. Cole, "Increasing Utilization of the Cost-Quantity
Relationship in hanufacturing," The Journal of Industrial Engineering,
(May-June, 1958), pp. 173-177.

SBIbid, p. 174.

 

 

 

(*Y"'\ 'vv
lube/uni...) e: 'u- ul-gux-.-.Li.1.

Ti'v' , ,-

Q‘. “7-. I
H’A.lL&J4h‘-i v‘qugJ-IKIAHUIAL

(‘7' 'T‘
Ida-u! ~44.

.'\’ .~ ‘ ‘
LLUxa U4. WI

Q - .u.-.,

iQLMLAVL-u.A-a$

‘ * ' "; "amp
-“LILLJ l‘b‘quU-L

v-

lu';i--.:-qv.u L) . lulu“.—

‘r1"

l-tx..J-' a‘LUiQ-..¢.l-CX

 

*'=v¢v>" m wmwmi N‘ ” ,r.‘ “
it"u‘iJu;J-l..L.-.u.) Dix-git J.LJ.JLL& ILL-LI-Liuw
3" 7 .. .. ,. '.‘ mr‘ ....‘- ,.. l I--- V" 'n -. r-~~—1--' 3 — ---\-.-.. . a- ' L--.,.-.
K‘ #0 ‘LL mkIL; LIAAKJ VUL - LJ—L- L-\——;A bl ad” J. L... Lug-\J-Au-;---‘.) -_..A 'M/ -54. LA..-\.,._.. v u.-_-

A y . 7‘. c 4- .
U V111 LL£~ LL\

0 '1
2.1.; pl: 4-“. :
veg,
AIO
"‘l A‘L’fi
LC “Lyi—
(U) 111:7 0 "01,1 LAC/(J91); J‘O‘U-l‘
.7 .1..-
Liz-Lbu.’
Y‘r ..-. ‘,,'..,.t
*r ,. .2 n- r V H ... .
to, allure-e curve
rm 4,
iOLu‘
(C) Cl: 1“ "TI O‘drio ’o “7
ax ~. v v. V‘. r1..- .-.L LJ. (Ay- U LA
n LOG Salty
YT. -- . 7
V {11“}. 1’s: U1. RAJ—

...l'a‘tSl} UL} liSC-LCL

(a. ntw is

)

the co s‘t—v. Lian tit;

 

'v.’ 2.1.1.

‘ ~'» '.
I‘i,_LLA. 9-1-01...

.
or uo

'. ,.
L.L b;

ULE..L.

‘ x\ "‘. (
~-4..1.va p u

~‘,, ‘1

d‘ u. LILC

/

“LL-DC?

‘v/

LC--u J

——

"vv
'v‘ V"\"1‘\ \
J—A‘ (JvkL (J

4.1;- -QU:\

\/;_LL K)...
J-

«-

l .
~— V

w w
\" ‘ "- «
iJ‘A-‘J.‘—-Lp--L\A

an; ‘
v- Krvl-U

P

,

\.l-.

X" 'r .‘J-
rvrdvli U
‘42

J;

)1.)

 

qu

Jar .

), -, V I.
I ."‘ "
rvA g.‘-,-.u
1..
’Krn’r

4-;

 

.Lk/L/

,.. (.4-
o-.<:3 uuu L."

~
F‘.._,.- , I

\u -nkvp’

 

‘,.-:~.f....J,-'_,~,. 7"
ALAN D‘_...£AU-x-xg “'a‘
r“: x“ 1“
I); i *IJQ a—L
J." y ‘ 1'1". .1 - ‘o ‘r\ f- N7 7(""‘ SI ’ i 1"“. \-:' F r:
I ‘L 0, (5C Ufi—Afi") J ‘A-*-/CJ vvd v .L VK'x-l..‘ A. I 'gil UV 1
~ J ‘—V! b.
.1'3_ CCU-Lag SUD'V ..L,i.b:: ..
‘Y 1 "t d -
I. .— ,\- .,. . ,.. ..
UL’k/J -L u L.) UL‘14\5‘~‘ \.£J 'f‘
‘ o - O l - o "
'1 ‘I ’1 "“V l‘ ' -~\ ~ ,’
4. uCili by «awn...» 54...»: '~
\ k II- _"_‘ '.
DOLJU CCniLLO]_ 4
‘, g , . -\ '
<"‘r.' ‘v-r-r » ”+31‘, .
LJ_g\-LLJ’:JLK.-ljd' CQ-A LJJ- 1J— 7“
3 ~ —-. r‘ 1.3 " r.‘ r“ -‘ j
UbOxiO- ._._V “.0 u p../,JL; .1.
fl
‘ +r7 5
.-O peat. L-q
r . -— c -' I ~ I a ,1 -
\ ‘\-_~ . v‘,‘ 7‘ ,. ‘ . . .. ,r , -- I . . l- -- r. ' _ 5 -~ -L /
UOL-L'CC: bug-t5 , “3:10 in. , ".L..1\J.i“-z'-t-EJ.;.L-O u MLa—Luu 'v—Oll O—L
‘ ,4. .‘ , " . I- '. .—, '. ' ., —" -. ~ a - ~- i'l r'."“\"u: V‘ l! ' '3
{Lu-«1‘ ALI-«LU LLLLL) Ll-L\31A&Jlé.t_iJ .51; ..\.-- .Lau LILLA—L 'L“c_) , .L—-\/
,. 'I' -‘-‘ ..1-. .J—A -. r ’5 .'-.\ .-.. »\ ,\ --)'f ' ~ -- . ‘7 v‘.‘ 1‘; - a ‘ ‘ r".
k}; .‘b-é\’v\_,_£ LJ_:..a—l* '__ ll ‘ L_'“_gk_, ./,. ,_4-.L,( . .(_Ad "I/ LL;A\./ u'n-l A) , P. .1— (Ir

 

Stanley E. Pryan

value concepts and collected data on its existence in a con

Professor :rvan related the time reduction curve phenomenon to

c ._ ~ we
cuner gooe-

manufacturing plant. Professor Tryan points out that there is a field

of buying in which competition ceases to be the important force in

determining prices. The contracting for special and non-s

equi

this

largely a iatter of negotiation. In two go iation, price is

tanda rd

pment which is made to cust01er specifications is an example of
type of procurement. The pricing of this type of goods becomes

related to cost to a much mat r extent than to the utility of he

particular item. Under these conditions, the method of es

tinating and

compiling cost of producing an item becomes all important not only to

the buyer, but also to the seller. In the case of the seller there

is a

multitude of production decisions which are effected

in which the costs are determined.

. - 3 J.
Professor Bryan presents time reduction oata

In terms of direct labor the first few units of

13:}, t} i8 me uliOds

, h p. .
a non—standardized product are ouilt ey less ef- iotent
methods and so with correspondin ly hi5her direct lalor

costs than later units. the ma anufacturer does not
consider the learning curve in his estimate he xMoul
cuote unrealistically high cost on the la ‘aor portion
of the contract. If the buyer is not aware of the
learning curve phenorenon he would accept the unreal-
istically high labor costs quoted as being fair, when
in reality they would not be fair at all The leg" rn—
ing curve actually helps to explain why a ouyer is
likely to get widely varying side that he coescn a
non—standard production run. Some co panies are
unaware of this learning curve phenorzenon. 1LL

 

E ' ,. f‘, _ it
JuStanley E. Bryan, "Value and the Learning carve, P

(September, 1954), p. 97-

which was expe

' A — .) f'f“ "- (L. I (3‘ .
a new production group in a large company 0 footxear pl‘nt

rienced by

- Elli)

urchasing,

particular manufacturer of footwear exterienced approximately 90 per—
cent slope time reduction curve.
Uorld‘fiar II Accelaration of Airframe Production

An analysis of Torld Uar II production experience has been made
”‘5

O J ‘ 1 I I I
by Crawford and Straus in 19h7. The study concerns itself primarily

with the accelaration of airframe production, but since the time reduc-
tion curve is an integral part of any production program, tine reduct—
ion curves are given a considerable amount of attention. The author
states that:

These industry and type averages will serve as
a valuable aid to mobilization planners in scheduling
production for a future h—day. The progress curves
obtained during the present study may be used as a
guide in conjunction with other planning factors to
predict, for instance, the amount of production
acceleration which might be reasonably expected for
a given production run, and the number of direct man—.1:6
hours necessary to accomplish mobilization schedules.“

, . ‘n \ _ ,. p 1 r 1 1,":
The data for this study was derived from the Source Pook Ol world Jar
5
ll Easic Data, and was based on the production data of one hundred

 

eighteen world War ll models. Jeighted average direct man—hours per
Pound at specific plane numbers were determined both for the industry
as a whole and for each type of airplane. The averages were arrived

at by dividing the sum ofihe direct unit man-hours for the total number
P

Of models available at a given cumulative plane number by the sum oi

the airframe unit weight of the same model. The average values thus

 

 

 

 

r’!’ . .
T" V Y_Yn A 5 wt - -
”J. R. Crawford, and s. Straus aforldl Mr Ll .Lccelala ILO__ 9; Alr‘
frame Production, Hq AKC, Dayton, Ohio, l/Y7.
Ibid, p‘ 59.

Source Book, op: cit.

 

-iV/_
determined were then plotted on logarithmic paper and a curve was
fitted to the points through the use of the least squares method. The
average time reduction curve for all models was 79.7 per—cent. It was
probably this study more than any other that established the 80 per-
cent curve as standard in the airframe industry. The average time

reduction curve slope for the major type of aircraft is reproduced in

 

 

 

 

 

 

 

Table 2.2.
TABLE 2.2
AVERAGE TIIE REDUCTIOT SLOPE
FOR w0flLD EAR II
AIRCRAFT PRODUCTION
SLOPE 0F TftE
TYPE OF AIRCRAFT HEHtCTIOT CJHVE
Fighters 79
Bombers 77
Transports 77

 

The weighted average curve for each type of aircraft are reproduced
in Figure 2.6. Fighter aircraft was the only model for which observations
were available beyond 10,000 units. It should be noted that the reason
for the flattening out of the average for all models beyond the approx-
imately 3,000 unit figure is the fact that data for the other models
were not available beyond this point and since the average consists of
fighter aircraft data and because this type of data is consistently
above average bomber and transport curves, a plateau appears in the
average curve for all types of aircraft. In the individual curve for
all fighter aircraft the time reduction curve continues to decline
even after ten thousand cumulative units are reached (see Figure 2.7).

The analysis concludes that the type of aircraft is all important in

 

 

 

SE .38 .cofimo 638 3233* .5.
.coflposeopm meg-:2 .3 2032383 HH Lax 3.83 fm 638.5 2.3 ..m A. .Eouxduo "co-Bow
mmESz mzjm
ooo.oH

 

 

 

 

 

      
    
    
      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- . _ a a a i fiI. . a a . .1« a a - a —
_.__..i .i ._._.. .4. i
i , . . . , . . . _ n . d . — . . . ~ * . . _ . fi _ . .
_ . . . . l . . _ _ . _ _ i . _
. . 4 . . . a . _ a _ . . . o H .
. . . . m . w ~ . m _ . . . _ a . A
. . . n . . u . o .. 4..., ....... 4 .-... I. o--.- . . . m 4...». . .I-w...-I Tn
. . . H. a _ ._ . . v o a
— o . .
_ w a i ~ _ . . _ 4.
r F — . e o o _ n k c M .
, . . . . , . . . . .
f . , . . . - . - . - . . .. . .. - . . . . .. . - I- r . .. . .. :-..-.. I! Ill-Ii...- . III-III: +1. J,-IIII-I.IoI-I-- . III-1.91-1!- o . N
_ . , . , i _ . . , . . . u . H . .
. . . . . . . . . . .
. u a . _ 4 . _ H _ . a ._ .
— . u A. . .9 .c . v o . _ w ..... A
H . r _ . . a U . .
a . n H .. . . . m . u
. . a . -
I o O - OI -I vI I O I ’ I 9 0 ..I6- I n. I... .IC..I Io-III .-nI-OIII-I Inllt-I'IIIII-IOI-Y .I.‘ lib-IIIOI I III .I.III-I..II-l‘I-I-l .Qll.|iu IIIII-I
. . _ -. . 4 . a . . . n 4 a m M II n
. . . u . . . .. u . a
_ M . m . . o. ... H .. . . u . . . a . . . .
. . _ u a . _. . .
w I o II. I n I o l-IOI II F. A o o II‘III 0,- IO! I .6 I-IIIOIn iv 0. bill» Til-fliv rl.ln.-.-O-Ivln.i.no llnl‘li-ll I.|ln '
_ . _ H _ H .. H U n h H 4 . . .
. ._ . . U . _ . . —
F o o 4 o 0 II .0, 0 I O a I I I II I - IAV. oI.-I.O.Inl¢Il-I§1. -I.O-l-I.fll' .IIO.III0IIII".II|-§IIIDI.QII0l-.1IIM . 0 III. b I. {M1 N n
w . . . . . . . . . . .
A . .. n . v w
.. . . . . + - . . - -- 3- -1- I- - a . . L---$II-+I-Im . -..-.I--.....I|I Ill-lit .. Lil-L infill-Ii».-. . I. O
. . . . . .
. . o + - o -I n -I .+ - - _ I III... p .+-Ila ...I..-+.--II.!.T..-I-I Lr,I .:IcI-I.9IIII.9-II.IOIII.. . J -1 h
_ u . . .
w . . . m- u o r 9I III 0 rlv n Inf l o o 5 uO-IIItIIlIn r....IInI-|41csllll.wlln 'I . f. r .JI.oI-I-O|ru-WI| 4I.Il IIA o
. . . _ n
w R . . I I v o I v I 0 n v I III I v o o b I wI II‘-| I- I0: III- *I a
fr \ II I It; III-I ||.|II.I o .I n ‘r u I h n p p ”I. IL . n.— h. '
._ . . _ . . . .. m . l . H . _. , .4. 4 L. - -
_ . _ i . i . 4 4 . _ . . i .....
i . . H
. . . . .. . . c . . _ .. . . .t I
. . + h H p . . 4 * .. u. H . . . . . . . . . .
- nn. .OIIKIII A n .. m. o . .o-I _' e t F, 0.1In In A . a . H In.¢..|v -..n- .nnotn I...U.O'IO-.IIICIL
. . . . . .- . n . u . . n o . w M . . .* o . - - II.
A v i. . . . . A_ . . i . a 4 . .L .- ,. . . . .-
. . . . . . r . . .. w .. v. . - - . . - - i
_ . o . . . . _ v . . . .
v I Il-lo I II I} -
4 . . . q u IIJ . . H H . - . N
_ _ . _ . . . u 4 . . _ o
. _ . . i u w H . . _ 0 n h . .
. . . o i -o -A . o I . .4 . 9.. . - . I In It 4 .
o . . . u n h a h u . , ._ u . .
. o . n U n . _ . _ . o . I
. . . . -.----»--II.I.-.:.-.-.--.--4III-.li- . .II I. I. n .. III!- M
. m . . . 1 . a . u n 1
~ . . . . . .
i. * . . . . . .. u . m . u ... _ m m . H II.
- - a . . L L. +3-.. . 54...-.- .IIIIrI-IIloI-I-III- V pip-It}? .--.I 4! . I...- I- if! '
H . . . . . . . . i ,
_. . _ v . o . . . . a a . v
n u . . . . .F a
7- I n .In. . o I .n c .. o. .I'IIIInoII- III-IO. -IIYDOOIO.|OIIIIOIIII¢.IOIII+IO.. n.1h . n . ,r w n
. . . . w . q . o .
i . u n w
. o o I .9 In an Inn 5! III- .IOII II I. 9 iv! I||O . -rllI| ”VII‘WIIIW. m Wt] o
i 4 _ a _ .
V n I I On II IIOI. n n IIIIIIInf I h- o .In..’| J. m IO.‘ N
v - ,. I- o - - II I I o- .o. ..In--. .A: 7.-.. If- IIl.l I’ll-u-u-I. + . 9 Ion- |.+|I- .7 III-III I III III-{L Q
- . - - . - I- L I- I? - . .I 3.: lIIIl-II I I“- n .4 .- . O
, n I I u - I I - .- . I I III-III ile...-I.lvul.¢nllIOIIIIf|II-. . a I '
. . w . -
_ _ _ M _
_ o n . t
a . . . . w .
o n u w . 4
. o e o w . e I I I [I IIII I V v o
_ . i h _
H A . . u . . . .
. . . _
. _ .
I f t o 0 O! I I. IOIIIIOIIIItOIIJI «III-0. .o 4i
_ , H H . . H.
_ . . . u
. . a — .
; o o 9 . c I . .. o t I 0
q o . . . c
i . . . . . .
, n _ n . . o
. _ . . .
u o I II I II. - IIOIII filillllinlv 1.. Y-..,Yn.-IOI.II.WII’IJI.-O- 4 f
. . _ .
. . _
q n . . .o .. . ”v - .
. - .. .. . . I- . . .-.-..-I-+I-IIII|I4..--....:.r:-.- III-LI. _ v
_ _. . u. . .. i . fl _ _ u _
_ . . . _ v . H w n . .
. . _ .
. - I . . 4.3-..I- ....--.--I...-IIIII-II-.-... III _.I . - - n
a . , . . _ . . n . . .
_ u H h h n w .
.. - I- - F I - I u -I I .-.».---I. -IIr.-..Il -.|.-. -1 a i . . .
4 u . . . A i q . .. . . . , u 0
. . . . . . . - . . . - . .
--I- r . . “I -r. -..-----...!--_-...- iIilI..:..I..I t n . . . . . . 4
_ . . . 4. . H h .. n h
o o n v I o .0. -IIII|o -i II.I-oI-' ’l- ..ln IOWI IMII-IVIIIII” IIOI.Innl-»I-IIIII'I- . h a
. _ H .. _ .
_ u . _ p n
I . ¢ .. I? o. . ~ .. I. n . .. In I- .-4.-|4-I IOIIITI..¢-.I-I-1 n . G
. I ’- -Ii- II-I I I n I L h .. » H "L“ b y n _ . w I H w _ .II- I - «I,» I. —8H
- I .v - .. .-
_...r-.n . r .- roar. r u. r N .omhwm v m N .mmhwm v m N —mnhch n N .

mmmmzsz m2<qm m>~a<qbzao nmsomqmm

.2 .Smooz 4.2 .§H< .8 9.50m SE

mm:o:uz<: Bowman q<sos me<mm>< omwmcamz
wow MESH-w

Filly-V-.. . . 4 ,I ill. I- ILI'
- . . .I: 1'}.-.

 

 

 

(INDOd 83d S'HIIOH'NVH

.cogofium mam-Cum no

’

cofiampoaooo< HH has capo: ..m .nmsmpum.ucw ..m .w .ugogzmgu

bawfi .oflno .cofmmo .Ucflfioo Hwflhvfifi LS.

 

"monsou

mmgz mzjm

H '

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

d I 1 1 1 BH U
. H . m H A 1 _ _ 4 a I a I. 4 4 I I I JIW .4 I4 I I.
. . . . - . .
. _ k F . q H — a . v . . . . o - . I o . . . .
. o I u . . . . . . . . o o . . ~ . _ . . .
. . I— . _ m _ _ . . o . o . . c . ~ I .
. . I . a _
_ . _ . _ . . . .
. . . . . . . . . a . . n . _ H M . . . . w
. . .
Y n I 0.. v- ..o- I ... 4: -I I o I I I Y o p: I . . . . . . . -
. . . u . - o o . c o 0 . o 0 o . o o o a v 0 o
. o _ . . . . . _ I . v .
4 . . . _ . . . _ , . N
- . .
. . , . . - . . . . , .
d...- Q-I I0..-I1III‘IIIIOIIIIIIII IIIIIIIIOIIIOII’ .I III, I'IIIIOIIII§ I.II 5 IIIIII.IOIIII|| III I o no IOIO -I.III-o I I- - -o- I I II I-I O . . . I - I I - - n I . .8
. . . . . . . . _. _ |
. . . . . . . . n .
I - I . M . . . . ‘ .
I . o I .- A I 4 o o o . . . .
I. .I . n . . . . . .
.I I III .. . . I . . . . . ,
III - I. I . .... Iz-IIIIII-I. .-II-II.--,- . ,. -. . . - .7 . . -- -- -w . - . . . ...-- . . . . . . . . . - . . .fl
. . u I . . — 1
. . . . . . x
I u n ‘
. .. 4 . w w n . _.
o D a
. “ ~ N ,
V .
.4 . I IIIO.IIIIII II”: I. 0. .o 'I..a-IIIIII.I .I.-IIIII O-I III-III - o I I .I o- oII A I o I n ..... 9 I I c .0. o o o I I O . "a
. . . . . . . . . . . .
n . 4 . . _
. . O . a . « fl
. . . . . . I
III 1 4:.- II .oI -0IIIIIIII0III-I9II-IIIIIOIIIIIIIII 114- .I I. o I o IIOI- A I I I I Q IIIIIII I I v I I .0
, . v
n
. . . _ . .
. . . . . . . - .
III-OI II- II. I H I . . . . . . . .
. I ~ A ' QIII-OII.IOIIIOIIIII nII IIII'IIIIIOIIII # I I: I I II IQI II III. II 0 I a I O o I o I I A
. _ .
.I .I L I II . . n . _ . w _
. . . . III-III.III.III§ III-I .Ill. .9 I- o. o 0 IoII II ...... I IOIIIIOII III W I I II- .I. .I o I II 0 I I III I + I .o. I a o h
. . . . _ . .
. . _ .
‘l 0 II. III II .In. - IIIIIII III: I III I . .
I I I o I o I o I: I O. .I- .o- o ...... 0 IIIIII - u I I. I I v I I _ .w
. 0 fl
1. .I- . - -..I. _ fl .. . . ....
. _
I I
. - I F I III- .I.I-..I I. III. w
0 O u C C I c ’
o o o . o . I .
. _ H n
9 . . o o o . a
I I I I o r I . . .
To 0... 0. .0I IIVI -f a II I O I I I o D .
9 Q g c O o 4 o
. u o o . v o . . I .
I n C 9 O n - O c
I . P w e . . . . . 1
III IfIIIo -0:- I0- I I I I o I I I I .- o ...... I t I I II- 4 IIIII II . f
. . . . n . . “I p .
. ~ 0 H . . . . . n .
. . I
. . . I w .. . n u
vIO n I. OI I I O. u - I w I o .
- . . . . . . I
. . . . . . . c
. . . . . u 4 . 4 I
WII‘IIIOI-O IIIIIIIOIIIIIIIQIII O I I + I IO I -IA I. II I II I It o-Il I III II I‘. I I. I 0 O I o 0 I I9 IIIII o A F.
. .
. .. . . , . v
. n n
w . . . . . _ . .
. u .
. . .. . . .
YIIOI-I tIOIIIIOII-I‘ III. 0| III-III III I O o o I 9 .o.IIIo. o IIIoII.I.III III-t-* n Io- .- v I I I0 I I..I O IIIIII .1 . A".
. . . . . . . . .
fl . . . . . .
. . .
. fl . .1
VII. III‘IIIIIIIII III.- I 4 I III .. I I IIIII II III-II... o- o 0.- 0 -0 I... . I I H
. .
. n n
_ _ . _
. . . )
YIO Y-IIOII-IIII.I§-I. O I... I-I .IIIIII II I I I I I III I I I I I II I n-IIII I I .I I a o. I I I I I o . L
. . . . .
. . - . . .
. . . _
I. I- .-4.---I-,:-.I-- . III... - - -I -4 . .- . - - - . - - . . -. . .n
. .
. . . II
II I I IIIOI. i D .I It - O . - I . I I I - .0 III I . L I . ‘
. '
I I I. II III I I I II . + u C
I 0- .On. II! III I I III Ill-I9.II-II-II.IIIIIIIIIIIIIIIIIIII-I r
. , .
_ _
. . a
r _
. . ..
I . . .
I I I o . . . I, .
. d a O
H . . /
_ .
. . r . .
I. I. .I-IOIIIIOIIII-IIIIIIIIIII.IIOII.It-II IYIO I n- I I o I. -III II I- - II o I L II III III I I o I I I . N
.
. .. .
. . _
. . .
. _ .
. .
. .
I. . -I--- ....... ---|-I.. . ..:.. . .4 - . . - - I - .. . ..
o _
.
, CC
I I I I I I I- I O I I I II I o .
. . . fl
— . _
. . *
. v x .I
v 6- 0. I I I. III III IIII I bIll -1 I o I c I II 9 II o I II o O I o I _ -M
h . .
A .
. .
TI...-.-I-.- -...- -. . -- . .- . . C
N . _
. h ‘
I5 I O I 0 II 0 II.‘ II I o I o .0 O O In ' o 0 I O O O '
I. O I an 0 O I o o. O O 0 IO 0 . I I I ' M IA
o I It-I 0 I.I o I o I I I o a I 9 I H l o I I o I y - o . J
.
. n I I I . I I I I . I I n— h

0

0:

\-

$9..

,wmnw m

95:52 az< 530x 4.2 .Egmmi
REES: $532 mzfim m>E§b§o “HE-0.3mm .5.
aghmgx m0 9,50%: mum mdDOII2<2 HUAKHQ ASN.0?

 

 

N-IN gUH-m

IIG

\
'5

UIOH‘NVI’I .LD'I

SI

GNIIOJ HTvId

 

-50-
influencing efficiency because the complexity, weight or access—
ibility, will vary from one type of aircraft to another. Other factors
such as priority status and production methods used, enter into the
picture so that the type of aircraft alone does not satisfactorily
explain the difference in the record man-hour efficiency between
models and types. According to the authors the other two important
factors are: (1) stage of development of the model, and (2) the
amount of experience that a given facility has had. A new model in
an inexperienced facility will normally cost more than a proven model
and experienced facility.58

In addition to the three main factors which have been found to be
responsible for deviations from the linear time reduction curve, that
is type of aircraft, newness of the model, and newness of the facility,
there is one other major factor which according to the authors, over-
shadows all others in causing variations. This fourth major factor is
described as the particular circumstances and problems that surround
production of each individual model. Some of the specific circumstances
and problems surrounding the production of a given model are listed
by the authors as: (l) the length of the production run, (2) whether
or not the model has been engineered for mass production, (3) whether
or not proven engineering was available when production started,

(4) whether or not high production was started from low production
tools, (5) introduction of design changes, (6) whether or not old

tools were available when production started, (7) availability of

58.1.1221. p. 84.

-51-
materials or component parts, (8) availability of experienced man—
power, (9) relative priority attached to a given model, (10) efficiency
of Operating controls, (11) frequency of scheduled changes and degree
of pressure attached to a program, (12) economical and uneconomical
use of outside production, (13) degree to which feeder plants and out—
lying areas were utilized in order to tap a wider labor market, (1h)
whether or not the plant layout was favorable to the production of a
particular model and (15) availability of specialized high production
machinery. The authors state:
Each of these factors affect direct man—hour costs.

In the final analysis, foresighted management can minim-

ize the effect of these factors, and can, in many cases,

even prevent their appearance as a problem. It would be

extremely difficult to attempt to measure the effect of

individual circumstances or to weigh direct labor pro—

gress curves and industry average for these factors. In

fact, in some cases it is not possible to isolate all of

the circumstances which affect direct man-hour costs of

a particular model. In spite of drawbacks, the industry

average as established in this section, presents a reli-

able picture of the relationship of direct man-hours per

pound to cumulative acceptances during world War II. They

include the cumulative effect of all the individual cir—

cumstances which surrounded the production program, for

each model.59
Qanpagy Publications

In addition to the many individual contributions to the time
reduction curve technique, many of the companies using this technique
have published manuals, booklets, or handbooks for the instruction of
their own personnel. It should be remembered that most of these pub-

lications, as a rule, do not contain any empirical data to support

statements made, but presumably, the statements are based on company

 

59Ibid, p. 91.

 

 

 

 

r N

-5,_
"experience." One of the earliest company publications availaole is
the booklet published by the Boeing Aircraft Company in l9h5, entitled
m *1 6O m1° 1 '
The a; perience Curve. lfilS short booxlet presents a conCise state-
ment of the unit curve, the cumulative average curve and the total
curve as they were used by Boeing Cost Accounting Department. The

authors make what is the first allusion to the hump curve in the

3

follow ing para Mr pn:

EXperience has shown that the 80 per—cent
experience curve is a prettyg ood average for
airplane production, although specific planes
or items may vary considerably from the 90 per-
cent curve. In many cases more than normal
preparation has seen made before starting pro—
duction, and this often causes what is termed
a hump in the curve, the first unit starting
low and the decrease to the next few being less
than normal until this flatter curve meets and
follows a normal curve. The method of handling
a hump curve depends upon the results desired.D

An interesting illustration of what is a man—hour is prese ented in

('11

this study. lne analysis of the man—hour as cumulative production
increases is presented in Figure 2.3. It shows that the time devoted
to production increases as cumulative production is increased. lany
of the activities which infringe on production time are eliminated

as the units produced are increased. In addition, this pamphlet
provides an excellent mathematical presentation and development of
the time reduction curve. The second publication by Boeing Aircra t

/
, i. 02 . a . , . . a
Company was authored by drown, at the :oeing Training department.

 

 

,
OOf‘ v f o 1
cordon a. Link and Don A. Ellis, The E} :perience Clrve,
(dichita, Kansas: Boeing Aircraft Comp anJ, December, 19“ 5)—
61" b
.L'JI'I, p. o
62.

ill-am F. frown, The .nprovement urve, (Iichita, Kansas:
W ‘ , 1'
peeing Airplane Company, Larch, 1955).

we: 3. . 3:32. .8 tawny: .33on . $3.8 m9§§w§w a:
.1} . . -. -. fiqwxzw 1.3.3 9.3» .. 983%

 

 

8% :1:

  

A 733
33 n.5,.

 
 

.
. M - i
_ . i
, . . .voR :¢ 00 on
, .58 o 36 a no roTtfisflvu a
"la — _ man he «50“ .3...— ar; B
., , V
tuinSOO: bondauouzn vs via-Id §«13 mrtoon‘rrd
‘9. 8362.255 65256 \\
onuocu Lute. uo {a '«wStlo . Jaguar}... 8: 4
loom-5 Can. 3 2.”:
.3“. u:- 5‘... ‘
.otum nor—63 so 98.13.3163 no 5:3 v0.2}: hp
2.5. 3 :r. «z: 3:. .
Lia-«Coal h. nevus-nu E 83 1:2qu a votes :3 M
. 5.3» dual §«ul:ul:im E 830560; 3 v0.3; 05k B

an €633 “d was “82.; a . _
eglhnnu Mud haaad 3mm: 1 a Elva Hui I4..-

e. d30112<§ < m. F<I>>

 

 

O

The manual presents the learning curve, as it is used by Boeing, in
relatively easy to understand form. An interesting statement is made
by the authors relative the rate of improvement as large cumulative
quantities are produced. In speaking of manufacture of automobile
bodies, the authors say:
If a manufacturer has built three million bodies,

and was building them at the rate of 500,000 a year,

it would take him six years to double his cumulative

total quantity of units produced. If he were operat—

ing on an 80 per—cent curve, his six millionth unit

would cost him 80 per—cent of his three millionth

unit, this would mean that it would take six years

to gain 20 per-cent improvement an average of approx-

imately 3 per—cent per year. Doubling production

when you make 350,100 or 1,000 items is accomplished

in a relatively short time; doubling production when

you are producing in the millions takes years.93
This is clearly contrary to the opinion held by the Woeing personnel
in the past, which was: after a certain number of units have been
produced, the time reduction curve would reach 100 per—cent slepe or
in other words, a horizontal position. Peeing now holds that where—
as time reduction continues to take place even after a large cumulative
numbers of production have been reached, this reduction will be in—
significant and may take a long time to realize. There is still
another paper published by the Boeing Company on the time reduction
curve. TAiS was published by the Boeing Airplane Company, Seattle,
Jashington Division, and consists almost entirely of the description

0 - . , . .
0i application of the improvement curve technique. It should be

noted that all three publications by the Boeing Airplane Company

63Ibid, p. 6.
64 .

v
1

Roy H. Smith, William C. Lansing, and Henry G. Eorton,
gmprovement Curve Handbook, (Seattle, Washington: hoeing Airplane
bompany, 1956).

follow the Boeing unit curve theory, which will be explained in
greater detail in Chapter 3. An extensive development of the Wright
type time reduction curve may be found in the publications of

5 . 66 l
Chance Vought and Northrop Aircraft. goth of these works were
prepared to train company personnel in the application of the linear
cumulative average curve, and would be of interest to those who
prefer the mathematical instead of the graphical method of derivation
of the time reduction curve. horgan is the author of the booklet
published by the Glenn L. Eartin Company,67which is also designed to
instruct its personnel in the use of the cumulative average curve.
It should be noted that this hartin publication is similar to that of
HorthrOp and Chance Vought in that all three of these company publi-
cations use the Wright time reduction curve which will be discussed
in greater length in Chapter 3. North American Aviation has two
publications; both of them were prepared for the instruction of the
purchasing personnel in the use of the learning curve in procurement

()9.
of subcontracted parts. The first work is entitled Improve Your Buy,

 

 

6r
9;. A. Rutan, Theorz pf the Learning Curves, (Dallas, Texas:
Chance Vought Aircraft Company, lth)
667.? T ,. 1 k . -,
u. A. Raborg, or., lCCflafllCS pf the Learning Curve, (iawthorne,
California: Iorthrup Aircraft Company, 1952).
67 ’7 " o v-fi . . .
A. a. Lorgan, ”experience Curves Applicable to the Aircraft
T n .. ' 1‘! , ,
tndUStrYa” (Baltimore, Larylanl: The G. L. Lartin Company, 1952).

 

 

Y"

L. J. Blume, and R. E. Norris, Improve Your Buy, (North
A . . .
American AViation, Inc., n.d.).

 

.. j L: -.

69
and the second one is Purcha ing gith the Learnigg Curve, he

 

latter being primarily a revision of the former. Fur chasini With

he Learning Curve is a concise statement of how a purchasing agent
may apply the learning curve to the many procurement problems which
arise in the course of his duty. The latest of company publications
on the subject of the learning curve was published in 1953 by

70

thonnel Aircraft Corporation. The distinctive features of this
company manual is that cDonnel Aircraft Corporation uses a straight
line for both the average and the unit curve. IcDonnell Aircraft
Corporation prefers to use the parallel lines because only one set
of progress factors are necessary, and can be used to determine
either the cumulative average or the unit average trend. The company
claims that the accuracy is retained because for estimating purposes,

,., . . .. 71, .,
only tne mid-pOint is oi importance. Tius, hcjonnell uses a straight
cumulative average curve and a straight unit curve. The unit curve
is displaced by the ratio of one minus the exponent of the basic curve
equation. Cf interest in this manual is the use to which the time,
rec luction is being put by KcDonncll Aircraft Corporation. The
authors state:

Lany different types of costs pertaining to air-

frame design, construction or manufacture appear to

fa ll in a pattern that is amenable to a progress slope

type of analysis. Engineering carry on, or cost after

first fligiht will plot to a line conforming generally

to the basic equation of a progress curve. Tooling

cost after peak rate tooling has been completed, includ—
ing costs such as tool maintenance, facility type changes

69a

L. J. Slums, and Donald Peitzke, Purchasingi .'iti the Learning
Curve, (Coluzeus, Ohio: Horth American Aviation,1953.
70
A. Anzanos, R. L. Field, and R. E. Lorenz, Con ntract Estimating
Proyress Curves Factors and Aaplication, (St. Louis: IcDonnell Air—
raft Corporation,1958).

Ibid, p. a.

etc., will also plot on this type of line. These
trends will hold true until the calendar time is
reached at which the project staff has been cut
back to an irreducible minimum, at which time

cost of engineering man—hours per airplane will
become constant. Certain types of material costs
will also varv with quantity based on an extremely
shallow progress curve. 4

The balance of the manual deals with the application of the progress
curve techniques to the various manufacturing prohlens.

host of the material in the company publications is rather
repetitious and similar to'hright's formulation, and, therefore, was
not discussed at very great detail.

'T“. l") 54-. 4'
lie hand ocicies

 

The Rand Corporation of Santa honica, California has prepared
several studies for the Air Force which should be of interest to

those interested in industrial time reduction curves. Alchian has

prepared a brief statistical report on The Reliabilit1_of Pro~ress
73
Curves in Airframe Production. In regards to the time reduction

 

curve, Alchian poses the following question: (1) How long does this
time reduction continue? (2) Can it be represented hy a linear
function on double log scale? All data used in this study was
derived from the Source Cook of World Var ll ?cSiC Data: Airframe
industry, Volume I, which was prepared by Air Nateriel Command at
wright Field. To the first question Alchian answers as follows:
In every case there was no evidence of any
cessation of a decline. This conclusion is based

on visual examination of the graphs presented in
the Source Book. No elaborate statistical analysis

 

72

Ibid, p. h.

 

 

Armen Alchian, Reliabilitv of Progress Curves in Aircraft
Production1 (Santa Konica, California: The Rand Corporation, 1950).

r ”T

c.) ;—
appears to be needed to answer this question, given
the available data. Whether or not the decline would
cease at substantiallv'larger numbers could not of
course be determined. W
In an attempt to answer the second question, namely whether the

linear function is aapropria e, the author finds that available

1
observations are not sufficient to be a good test of the linear
hypothesis. Since no acceptable alternative hypotheses were avail-
able to the author, he felt it would be best to postpone such tests
until adequate observations were available. It should be added,
that coefficients of correlation for the accumulated data exceeded
'5).

.90 in sixty cases, e s the model facility combinations, and exceed—

ed .30 in at six other cases.

}_.I
.4
Q)
C)
(+

75

Another Rand report which was prepared by Nof nan attempts to

‘

evaluate the modified form of the aircraft progrsss function, as
suggested by the Stanford Research Institute. It was Yoffman's
purpose to determine whether the progress curve, as suggested by
Stanford's Research Institute and which includes the iota factor, or
in other words, includes an additional parameter, is superior over
the original, and the more simple form of the curve in terns of the
' .n m1 ' b
fit oi the curves to the observed data. ine equation Y : ax was
fitted to several series to which Stanford Research Institute had
applied their formula containing the Feta factor, which reads Y = a(x+“) .

The square logarithnic deviations from the several curves were obtain—

ed and compared. Hoffman concludes that:

74

75,.

1.
Progress F nctions, (Santa honica, California: The Rand Corporation,
October 4, 19505: p. 6‘

 

 

Ibid, 0. 6.
. S. Koffman, Comments 2g the Kodified Form of the Aircraft
u

 

l

J

.. r)_
/

"/
There appears to be little basis for choice

between the restricted form of the Stanford Re-

search Institute curve and the original form of

the curve. 3
In several cases, the inclusion of this third parameter or the "3”
factor did result in smaller sums of squared deviations, but because
of the assembling problems, Hoffman feels that it is impossible to
determine whether the improvement justifies the fitting of the "9"
factor or even whether the Stanford curve is a true functional form
in this case. An analysis of the residuals about the curve shows
that these are serially correlated and follow a pattern which indicates
that the Stanford curves are not sufficiently convex upward to des-
cribe the series.
77

h

iand studies was prepared by Harold Asher.

A

one of the most recent
Asher attempts to show that the time reduction curve in linear terms
does not represent an accurate description of the relationship between
unit man—hours and the cumulative output. To show th t the time re-
duction curve is non—linear after a certain cumulative production
number has been reached, Asher examines hourly data for a number of
different departments. It is concluded that linear approximation is
reasonable for all departments for an initial quantity of airframes,
however, the different departments exhibit non—similar slopes for

these linear segn nts. Asher states hat:

76

77harold Asher, Cost-Zuantit" Relatioiships in he Airframe
Industrv, July 1, 1956, 9.2- £11.:-

Ibid, p. l.

 

 

~60-

This act alone is sufficient to cast doubt upon

the validity of the hypothesis that the sum of the

four shop group curves is linear.
In addition, the author claims that data for the departments which
were considered by him showed a departure from linearity in many
cases even before unit 1,000 was reached. Asher then proceeded to
sum the department curves. The sum unit curve shows that it begins
to level off at approximately unit 125, and the author claims that
if a linear extrapolation was made between units 100 to 1,000, the
estimating error would be about 25 per-cent.

It is safe to conclude, on the basis of the

admittedly limited samples examined in this study,

that the conventional linear progress curve is not

an accurate description of the relationship between

unit cost and cumulative output. deyond certain

values of cumulative output, both the labor and

the production cost curves develop convexity.‘
The above conclusion is probably premature for a number of reasons.
First, Asher's analysis of the nine fighter aircraft models is too
small a sample to draw any definite conclusions. Second, although
mathematically it is entirely true that downward sloping linear
curves which have different individual slope value will eventually
cross, and, therefore, the total will level off. This overlooks the
dynamic nature of a production function. In direct opposition to
the conclusion made by Asher, werld War II production experience

even in the cases of fighter airplanes which were built in large

numbers does not show a convexity at later stages. This has been

78Ibid, p. 97.

79Ibid, p. 129.

-151-
substantiated in th Hoffman study in the above paragraphs. Then
static assumptions are made relative the production function, we may
well expect a limit beyond which there is no improvement, and the
curve becomes horizontal. In his conclusions Asher states:
The linear curve is also useful for making
extrapolations beyond unit 300, provided tha
the number of additipnal units to be produced
is relatively small.“
IT d P". - Y o fa o t in t1“ ‘ . (‘0 7" r. _. tflr
he oes not give any speCi ic uni where he curve assumes conveXi .
In another point, Asher states that:
It is clearly a matter of judgment whether
or not in a specific instance the linear curve
is apprOpriate.“
Neither the Air Force nor the airframe industry have accepted Asher's
views on the linearity of the time reduction curve.
The Stanford Studies
Under contract with the United States iir Force, Air Materiel

Command, the Stanford Research Institute made a study on the

' J

 

o u . ‘ _ T-fi‘Vy’r‘y 41 ' _: V 4,1.
helationsh1»s for Deterninins the thinum ax)aisioilitv of the

._
— A

. . “w - ' J.
Elements _2 Peace-Time Aircraft Procurement riouram, this study

IE.)

was undertaken to determine the means of measuring the maXimun rates

in aircraft production programs. Since thy maXimum ex anSibility

the rate of manufacturing time

...L

rates depend to a large extent on
' 1. O 1'-
reduction, a decision was made to analyze the direct man—dour tlje

reduction curve. According to the final report the progect has

resulted in:

 

$0
” Ibid, p. 149.
31 .., do

Icid, p. p).

 

An improved relationship involving direct
man—hours, airframe unit weight and accumulat—
ive acceptances.U2

An attempt is made to show th at al H‘nou h hie conventional
formulations of the time reduction curve are represented by a straight
line when plotted on 10; :arithnic scales a new characteristic called
the "3" factor which when included in the formula, seem to describe
the exis Mi ng empirical production data more adequately than the
straight line function for either the unit or cu ulative average
relationship. 3 The ”3” constant, which he study suggests, is the
measure of all complexities that exist in any plant relative to a

SiVen model before the model is actually produced. The thirty cases

studied led to the conclusion that the data tended to deviate from a

scales and that it

0

straight line when plotted on double logaritnmi
tended to follow a convex shape in the upper area, particularly

during the earlyp part of the progran.

. , . 3 1” fl C
There are only a few cases where time reduction curve data can

i ' 'm ‘ ‘ '9p': +
be described more adequately by tne introduction of tne cons+ an

my.

new ,
- - - a. ' 12*" T1“ yiie
into the conventional time reduction curve equation. it t r

reduction curve users report that in these cases a straight line 15

~ - ‘ r '" ~4 I m a ' ” “s a ‘ free
not used, but neither is the YStanford e1uation. tau 11y, a

 

21..” a: .51 +.. ,0
2Selation r Deter inins the LquPII hi an: ‘ i I of
1

“295 w
t} T“lF‘V—Wt of a Peac 'me aircraft TIJCJFPW nt Prosrin, Stan o d
.e v .L V 1 ' _ '\ :L]? . .
Research Institute, Sta nfore, California, Aubust, (l , ,, p

O 0
U3 Wa ilanation of the

.th

search Institute,

J4

fl.- . «’1. V’n-L‘ n’IQ'F. (1-
An improved Rational ENL' . ne ica

1 ~. Z’\
P “res Curve in Airframe Production, Stanford it
L . f)“ ) )0
Sta nforci ,California, Aubust, (1,'L35,o p.

”4v
V HOffman, 920 Clot , AI). 20

‘

 

./_ '7
-b) )—

hand curve may ae fitted to the data. He nay only add at this point

that the Stanford equation has not achieved popularity among the

users or the students of the tine reduction curve. Hoffman's analysis

of the modified Stanford equation certainly casts doubt on the hroader
'3. r

application of this variation. 2

S um a rv

The reduction in time requirement experienced as quantities
produced increase is one aspect of economic progress. Industrial
psychologists have used the term learning curve to describe on the
job learning of an individual worker. tany companies still use the
tern to denote the tine reduction curve. The conventional shape 0;
a worker's learning curve is a rapid rise at the beginning, then a
slow rise until a plateau is reached. fihether there is a plateau on
a long—term basis is debatahle. A number of studies have shown that
for the periods observed a definite leveling off in learning of an
industrial task was evident.

This study shows that tine reduction takes place over extended
time intervals and also after large quantities of a product are
manufactured. It appears that individual learning on the part of
the worker is an important factor in the time reduction during the
early stage of a production program. As yet the factors and their

. . -_ R ' ' Y‘—
influence on time reduction have not been measured. available infoi

. . ,. - a L- . , , rihuted
mation indicates that the time reouction curve cannot be att

 

 

-64-
to any one factor of production. The curve summarizes progress or
"learning" of the organization as a whole.

Although the manufacturing time reduction curve has been dis-
covered in 1922, it was largely unknown until World war II. Wartime
airframe and shipbuilding man—hour data was studied by a number of
writers. Each study tends to substantiate significant time reduction
as quantities manufactured increased.

T. P. Wright is given credit for originating the time reduction
curve. His statement that cumulative average man—hours per unit
decline by a constant percentage every time the quantity produced is
doubled, is still the most popular formulation in existence. A
number of attempts to change the concept have not been successful.

A recent regional survey reports that 61 per—cent of non-airframe
metal product manufacturing companies contacted use the time reduction
curve in manufacturing planning. The curve has been reported to exist
in construction machinery, snoe, and other production situations.

In Chapter 3, theoretical considerations of the time reduction

curve will be discussed.

The Time Reduction Curve Cheory

THE RETICAL COJSIDERATIOY OF

CHAPTER III

’5
id

TIIE REUUCTIOT CURVE

Analysis of World War II production eXperience has shown that the

cumulative average hours per unit follow a predictable relationship which

results in a hyperbolic function when plotted on arithmetic paper, and in

l
a linear function when plotted on log-log graph paper. The theory of

the time reduction curve most frequently in use states that as the total

quantity of output of a given product doubles, the total input of direct

man-hours necessary for the production of the second half of the total

declines by a constant and predictable percentage. Thus, if the first

unit requires 1,000 hours to produce, the second unit will require 900

man-hours, the fourth 640 man—hours, and 512 man-hours for the eighth

unit (assuming the existence of an 30 per—cent cumulative average time

reduction curve).

Unit To

swore-

(\

O
16

32
64

of Product X

 

Reguired Nan—hoursgper Unit
1,000
800
640
512
#09.6
327.7
262.1

 

The cost per unit may be either the cost of individual unit, or it

may be the average cost of a given number of units. The first is known

as the unit average time reduction curve, and the second as the cumula—

tive average time reduction curve.

 

J. R. Crawford and E. Straus, pp. cit., p. 56.

-65-

-66_

The fact that as a particular operation is performed repeatedly the
time required to perform this operation declines has been known for a
long time. The manufacturing organization beginning with the individual
employee becomes more efficient each time a process or operation is re—
peated. There are many factors which increase the productive efficiency,
and this may explain the recurring decline in direct man-hours. We shall
discuss some specific factors in greater detail in Chapter 7. Among the
more important causes of declining man—hours appear to be job familiariza-
tion by workman, improvement in plant organization and coordination,
development of more efficient parts supply system, and development of
more efficient tools and production techniques.

The time reduction curve is merely a statistical tool which is used
in some firms to predict the various requirements necessary to produce a
given amount of goods. The more times a given task is performed, the
less time it takes, but time reduction becomes less with each successive
unit.
Assumptions

Although the present writer has not been able to find any explicit
assumptions in the presently available studies, a number of them are im-
plied, and a user of the time reduction curve theory should be familiar
with them. First, the above formulation of the time reduction curve
theory assumes that the time reduction trend once established will con-
tinue for the quantity of production for which the man-hours are being
determined. That forces responsible for the improvement tendency in the
past will continue to exist in the future. The second assumption which
must be made is that the unit on which factor effort is expended remains

constant throughout the program. This would exclude any major changes

 

 

 

VIII} V le’ bL

.0..- 3m

      

Ampmc 1on vmfivombmv

ma 9 "wouzom
mason cauchpaea cc o>uzo campedpmh asap peso u c

fin 6E

1”
C

do
on n.

    
 

on am a

 

e;-

  
 

‘Nlu‘oxuomimck

 

.u‘

 

“I

 

 

.
‘a

 

__‘.

  

-63-
that would necessitate either an increase or decrease of man—hour require—
ments per unit. Third, it is assumed that there are no significant changes
in labor turnover.

Fourth, it must be assumed that while production is in progress,
there are no time breaks in the sequential units. This excludes the
possibility of any unplanned changes in the production flow. An example
of this may be a sudden termination of a defense contract or a major
accident which would seriously affect the normal production activity.

How reasonable are these assumptions? A detailed discussion and
empirical analysis will be taken up in Chapter 5 of this study; here we
shall only make some of the more evident observations.

It is probably reasonable to expect that some of the forces which
were at work in the past to continue in the future. The assumption that
the unit on which effort is expended remains unchanged is made solely
for convenience and is seldom true in practice. The turnover of labor is
usually unchanged except in cases where a program is accelerated, and a
large percentage of new inexperienced employees are hired. hajor inter-
ruptions of production such as major accidents, should be considered as
exceptions, which do not happen with predictable frequency, and may well
be disregarded for our purposes.

The Time Reduction Curve on Arithmetic nger

The time reduction curve may be illustrated on arithmetic graph
paper. For this purpose, let us consider the 80 per—cent slope time re-
duction curve. Table 3.1, above, shows the man-hours required for a
hypothetical product as the quantities produced are doubled.

Let us plot these man—hours expended on arithmetic paper (Figure 3.1).

A connection of the plotted points results in a true curve and illustrates

 

-69-
the reduction in man—hours as succeeding units are produced. The reader
may note the sharp decline in the curve at first, and then a gentle slope
downward as the percentage of improvement is distributed over a larger
and larger base of production, and an increasing period of time between
doubled quantities.

The horizontal axis of Figure 3.1 shows the number of items that have
been produced. The numbers along the vertical axis of the graph repre-
sents the required man-hours to complete each item. From the graph in
Figure 3.1 we can easily determine the number of man—hours required to
produce any unit between one and sixty—four. The graph could be extended
so that the curve may include any number of units desired. Even though
the percentage of improvement between doubled quantities is constant in
Figure 3.1 (30 per-cent), this fact is not apparent from simple observa-
tion. Another disadvantage of the curve, as portrayed in Figure 3.1 is
found when we attempt to extend the curve for several thousand units, the
graph paper would be overly long. Also, construction, interpretation,
and projection of the curve on arithmetic paper would be mostcfifficult.
Referring to Figure 3.1 again, the sequence or unit numbers increase in
geometric progression, the variable factor decreases in geometric progres—
sion. Consequently, to interpret the time reduction curve would require
knowledge of analytical geometry and extensive computation. For these
and other reasons the arithmetic paper is seldom used to present the time
reduction curve.

The Time Reduction Curve on Log-Log Graph Paper

The major difference between arithmetic and logarithmic graph paper

is that logarithmic paper (log—log) is so designed that the vertical and

horizontal distances between doubled quantities are equal. That is why

 

 

I!

 

—?-x

p.

 

5 .‘dl‘ .r, l

 

 

 

 

 

 

 

000p Una. a; ... : .-. mm
A i 1 - i a w i
_ . w
A
- _ A -
_ _ .
i F _ _ . _
u -. o . . .o.. . ofi . . . .
m _ «awe HmnwsmEsocszm H.m q~.ap -+ .4
_. m -. . . . m -
v + O o .. o . . n . u m. o O. a .o.
.e and. Saginaw-”fl. 3 m...”- ud 9L4.“- aamhm-m manage A430 sued .Qm. amp. .. .n..m 3.3.3 .-
. O . I u u I
.,+,.-..D. I. o . o . . v . t . . . ‘ . o o . n - .
d. 0
w
_
h
-.!
x. - H
o [If
M ‘ (D
, fl 4/
,. . vi.
- - //
V .ll.’
[1!
., 4/
r 4/;
H
I . |-I tii’x» lull . | I. I0] I II I l Ll. .i: | . I It . 'l Ii ill n T A 1“: «I s Illrib II I Ii 1 I}
n. H r T I \ . C o. W h F . .. .L n; m. N _. - - r p. n. F M r 2. . r
- |!
J ’

 

,---_-A_.__ :- .—-— -____._,_.__ -

. -...- \_‘—...._—. - _‘.——r

 

 

"P

 

 

-71-

when a case of constant percentage of improvement is assumed the
curve becomes a straight line on log-log paper. The distance between
one and two is the same as the distance between two and four, or one
hundred and two hundred, or one thousand and two thousand, etc.; this
is so on either axis.

Figure 3.2 shows that hypothetical data assumes a straight line
when plotted on log—log paper. A line in this form is not difficult
to project and interpret. The line may simply extend the approximate
time required for any unit read. The curve in Figure 3.2 appears to
be decreasing too rapidly. This visual illusion is actually due to .
the fact that on the log-leg paper the scales are expanding, and the
curve is declining at a decreasing rate, and therefore, for practical.
purpose it approaches zero at infinity. hathematically, it is quite
impossible for the time reduction curve to reach zero since this
value does not exist on logarithmic paper.

The Boeing Unit Average Curve Concept
There are two basic approaches to the time reduction curve
2
technique. The first may be called the Boeing unit average curve
theory, and the second the Wright cumulative average curve theory.

T19 . .‘ . 3 .
-ne unit average theory used by Boeing 18 based on the pro—

position that there is an improvement of 20 per-cent between doubled

 

2
fl . The name Boeing unit curve theory is used primarily because
peeing 18 the only major firm to use the concept.
For a detailed discussion see Improvement Curve Handbook,
1" ' . r‘
peeing Airplane Company, 1956.

-fl_a/
quantities. According to this formulation if the first unit has cost
one hundred man-hours, the second unit will cost only eighty hours, and
the Cumulative average man—hour cost for the two units will be ninety
man-hours. Column two of Table 3.2 shows that the rate of improvement
is constant between doubled quantities. The foregoing may best be
illustrated through the use of a table and a graphic presentation of
the values contained in Table 3.2.

The values for Table 3.2 were obtained through the use of the
factor tables in the Boeing Handbook and simple calculations. he
factor value may be read for the various time reduction curve slopes.
The cumulative total cost is merely a summation of the individual unit
cost. The cumulative average cost column, is obtained by dividing the
cumulative total cost column by the cumulative number of units produced

In the absence of readily computed factors for the different slope
time reduction curves, the values in Table 3.2 may be derived by the
use of the following formulae:

1. The unit curve values may be derived from

Y=axb (l)

where

"x“ is defined as the cumulative unit number.

"a" represents the direct man—hours for unit number one.

"b" is a negative fraction which defines the slope, or the

rate of improvement;

"Y" represents the direct man—hours for a given unit number.

Thus when X equals 1, then Y equals a.

2. The cumulative total equation is:

cumulative total = a xb+l. (2)

’in
This is merely the integral of the unit curve equation.

 

-72-

TABLE 3.2

If A T TYL‘S P‘AT) ”1""? '3 “’77" Y."- Y? TTm r‘IY')‘_f’..‘
‘13;.'.Jx...1 \.J-lv A -xJ .14. ‘J U .L- v-‘.L‘I._J

 

 

UHIT CUKULATIVE CUMULATIVE

031T to. 30023 TOTAL 20223 AVERAGE 70033
l 100.00 100.00 100.00
2 80.00 130.00 90.00
3 70.20 250.20 33.40
4 64.00 314.20 73.55
5 59-56 373-77 74.75
6 56.17 439.94 71.66
7 53-45 “33-35 69.05
8 51.20 534.59 66.02
9 49.29 533.09 64.83
10 47.65 631.54 63.15
20 30.12 1,043.50 52.42
30 33.46 1,402.00 46.73
50 23.33 2,012.17 40.20
100 22.71 3,265.08 32.65
200 8.16 5,272.00 26.36
500 13.52 9,334.73 19.73
1000 10.82 15,367.09 15.87

Source: Unit hour data obtained from the Boeing Tables of curve slope
values, published by the Boeing Aircraft Company, Wichita, Kansas,
(n.d.), columns three and four were computed.

 

 

 

 

-73-

3. The cumulative average values may be obtained by dividing
the cumulative total equation by the number or units or

b

C.A.= a x

1

In practiZei analysis is confined to the graphic method. This
consists of constructing a curve for the applicable slope and then
reading off the values at various cumulative quantitites of output.
This method does not yield exact accuracy. It is believed that only
three point accuracy can be obtained from reading logarithmic graph
paper. In many estimating situations the graphical method will pro-
vide sufficient accuracy and, because of its simplicity, is the pre-
ferred method.

When the Table 3.2 data is plotted in Figure 3.3, it is obvious
that the unit curve and the cumulative average curve take different
paths. The cumulative average curve is always above the unit curve
since the preceeding values always tend to raise the cumulative aver—
age curve. We should note that even though the cumulative average
line is plotted on log—log paper, it does not begin to approach a
straight line until about twenty units have been produced. At the
beginning the cumulative average line in the Boeing system is
actually a curve, and therefore is more difficult to plot and interpret
than the unit curve. The projection of the Boeing cumulative average
curve can be easily distorted in the initial stage of the curve, and
its use is undesirable when projecting up to twenty units. Mathemati-
cally, the cumulative average will never exactly parallel the unit
curve, although it will approach it closely after twenty units have been
produced so that for practical purposes they may be considered parallel.

The important point to keep in mind is that the unit curve is a straight line

 

"team when Lem om um uhfifidnmm .mnm: Hm”.

mm>mmp rempnmmmn and.

             

- u I I. :1]
«Full ..» L n-
:TKL i X I rut-331i-

.‘Au El I ism-ll»

iv
u
2
0
2.
fr
oi
0&-
O
'(‘T
v:
r—j.
.‘J
'W'
E4
6;
m
L‘
E;
b

when plotted on log—log paper and the cumulative average line is developed.
The Wright Cumulative Average Curve Concept

The Wright cumulative average curve is based on the hypothesis
that as the number of units produced doubles, the cumulative average
man-hours required to manufacture the units will decline by some constant
percentage.“ Table 3.3 below illustrates the values for the Wright time
reduction curve theory. Assuming an 30 per-cent slope of time reduction,
if the first unit cost one hundred man—hours, the second unit curve will
cost only sixty man—hours; the average cost for the two units is eighty
hours.

When the unit cost and the cumulative average cost columns of Table
3.3 are plotted on log-log paper in Figure 3.4, it is the cumulative
average curve that is represented by a straight line from unit number one.
The unit line is now curved for about the first ten units of output.
After that the unit line approaches a parallel position, without actually
ever reaching it. Thus, using this concept of the time reduction curve,
the cumulative average curve is now the preferred method of projecting
the man-hours for the first twenty units. For those preferring the
mathematical method, the following equations for the curves based on the
Wright concept may be used:

. . b .
l. The unit curve values may be derived from: V=(b+l) ax with

a.

all the symbols still representing the same variables.

. . , b
2. The cumulative average values may be derived from: f = ax

It will be recalled that this formula is identical to the one used to

derive values for the Boeing unit curve, and this is possible because the

 

The reason for this designation is that this concept was originally
purposed by wright, and is still in use by most firms.

-76-

TAPLE 3.3

VALUES FOR THE WRIGHT 30 ER-CEVT CUKULATIVE A”T7‘”“ "2V3

.- ..1. 44.61.) t.

 

 

 

UTIT CUPULATIVE CUlULATIVE
UTIT EO. HOURS TOTAL FOURS AVERAGE UCUPS
1 100.00 100.00 100.00
2 60.00 160.00 80.00
3 50.63 210.63 70.20
4 45.37 256.00 64.00
5 41.82 297.8, 59.56
6 39.19 337.01 56.17
7 37.13 374.14 53.45
3 35.46 409.60 51.20
9 34.05 443.65 49.2?
10 32.86 476.51 47.65
20 26.06 762.42 33.12
30 23.02 33.46
50 19.31 1,019.14 23.33
100 15.42 2,270.62 22.71
200 12.33 3,632.99 13.16
500 9.17 6,762.32 13.52
1,000 7.34 10,319.71 10.92

Source: Cumulative average hours obtained from the Boeinngables of
curve slope values, published by the Boeing Aircraft Company, Uichita,
Kansas, (n.d.), columns two and three were computed.

 

 

Hunszz «Hun
OOH

 

 

 

lumps? .0650. 3.1181

1

  

 

OOOH

I . In. II
swis... .v vw ‘-
- - . .. I...-<-...i!.3 '

 

-78-
cumulative average curve in this formulation is a straight line on
logarithmic paper.

3. The cumulative total equation is still: c.t.= a x b + l.

b+l
The graphic method of computation suggested in connection with the

Boeing curve, holds true in the case of the Wright curve as well.
The Alternative Time Reduction Curve Theories

Examination of Table 3.2 and 3.3 will reveal that the straight
line values in the two theories are identical. Plotting the values
contained in Column two of Table 3.2 and Column four of Table 3.3,
will result in a single straight line for both formulations. This
result may be observed in Figure 3.5. It will be recalled that al—
hough the value at specific quantities and the position of the
straight line is identical, the Boeing theory claims that these values
are for the unit line, whereas the Wright theory assumes that the
straight line represents the cumulative average values. It is evident
that there will be a different result in the cumulative average and
cumulative total values when an 30 per—cent slope is assumed and when
both methods are applied to identical unit number one value. The
cumulative total and the cumulative average values at 1000 units are
about 50 per-cent higher in the case of the Eoeing method. In other
words, given an identical unit number one value the wright method will
show about 50 per—cent greater improvement than that found in the
Boeing method.

The large difference in cumulative results is primarily due to
the fact that in the above example both the unit and the cumulative

average curves are treated as linear functions. This is illogical

33:36

  

,
..... a i
i
i
M
Q
m
o
h
a
m
_ m
.
U.
or ~ 0
7. m
n
:1—
9
v I 1
m n
a mi
N no.
a
m
8....
N
03.

- ¢ . a n. I...
.Ecw. ,.v .2 .A
' I - .0193 I X n .3; ’

-80-

from the mathematical point of view. 'Nithout referring to either
method, it may be stated that the straight line may be fitted to the
unit or cumulative average data. When this is done the two straight
lines will not start at the same point on the vertical axis. This
result may be observed in Figure 3.7, where the least squares method
was used to obtain the unit and the cumulative average line of best
fit. It should be noted that the unit and the average lines are
approximately parallel so that if these lines were used for estimat-
ing purposes, similar results should be obtained. (For proof that
similar results will be obtained see paragraph on estimating with the
alternative methods).

0n the other hand, when an assumption is made that the unit and
the average curve is linear and starting at the same point on the
vertical axis different estimating results will be obtained. It can—
not be otherwise because the same equation and slope percentage is
being applied to the unit line in the Boeing and cumulative average
line in the Wright method. At unit number two the Boeing method
shows eighty man—hours for unit number two, and ninety man-hours as
being the average for units one and two. Using the Wright method we
get sixty man—hours for unit number two. The average for the first
two units is eighty hours.

An observation of Figure 3.5 indicates that the unit line in the
wright theory and the cumulative average line in the Eoeing theory
are curved for about the first ten units and tend to parallel the
straight line in each case after that initial quantity. The exact

quantity of units at which the two curves in either theory become

 

 

.---.

’ ..
7..-----_._.‘

........

_

.11.,1 111‘

.l | IIIII‘,+I.IQ|AWII.V|0|‘|

a

.‘11‘III

8-4-» 11-1-1 .:

S

 

 

parallel may be determined by simply dividing the unit (or average)
value at a given quantity by the unit (or average) value at half that
quantity.

For example: To find at what point the unit curve in the Uright
formulation is approximately parallel to the cumulative average curve
the slope at various double quantity points may be obtained. Jomputing
the slope for values contained in Column two of Table 3.3, using the
above method, we get a 60 per—cent slope between units one and two,
75.6 per—cent slope between units two and four, 73.2 per-cent slope
between units four and eight, 79.1 per—cent slope between unit eight
and sixteen and 30 per—cent slope between units sixteen and thirty—two.
It is evident that the two curves tend to be parallel after a number
of units have been produced.

As a matter of practice, despite the differences in the initial
stages, most firms treat the two curves as parallel. The reason for
this practice seems to be that when differential calculus is used to
determine the unit line when the cumulative average line is known, the
unit line obtained will also be a straight line and parallel to the
cumulative average line. The exact position of the unit curve in this
method may be determined by multiplying the man—hours at given quantity

by a factor. The factor is obtained by subtracting the slope exponent

1"

from unity (or l-b)-)

The above analysis may be summarized as follows:
1. There is a significant difference in results obtained when the

Boeing and the Wright methods are applied to an identical unit number

For more detailed description see Relationship of Wright Cumul-
ative Average and Unit Curves, below.

,23_

2. The difference is in that the same equation is applied to the
unit curve in the ioeing method and the cumulative average curve in
the Wright method. This, in effect, assumes that both lines are
parallel. Actually, one or the other must be developed; both cannot
be straight lines. When actual data is used to project with either of
the linear formulations, they start at cifferent points on the vertical
axis, and the estimated results should be similar.

3. The unit line in the Uright method and the cumulative curve in the
Boeing method are curved for quantities of about thirty units, and
therefore, at this stage they are not parallel or of the sam slope
characteristic as the straight line.

4. After thirty units are produced the curved lines will evidence the
same slope as the straight line (within less than 1 per-cent) and may
be considered parallel to the straight line.

Comparison of Curve Characteristics

 

A question may be raised what difference in results, if any, will
be obtained when the foeing and the Uright method is applied to the
same data. Eleven curves were fitted to a straight line through the
use of the least squares method. The line of revression was computed
using the Wright and the Boeing method. The relationch e of actual

A-
A.

.L V . . . . . . .
data values to the straight line Characteristics will so found in
Table 3 b n m,- an. a i1_ 1- + - : --w- .

.r. A comparison oi tne curve cnaracceristics ltClCBtCS that
Significant differences exist. Both the Uright and the Peeing theories
assuymz't a ' P ' -- . ,-- :¢,. -

hit a linear lunction Mill result on lobdrluLHCth scales.

anCh of the two methods will result in a better fit of a straieht
'k‘.)

. 7 T ,. %, fi_ , . , .. .
line. in nine of the eleven cases, the fright method, wnicn assumes

r;1 jTfi 2,

4.4L )lJJ o T’
{171; "17‘ 7 ‘7‘ ‘fl’fi*‘f 1 C11“; ‘J‘_1 m- r\"j,r ”\F'W‘ "1T5N11T/‘1 and")
.. 'i:_: -QJULKJLLUH u.-. _: J JLLL.L'..\J .._:u....‘- .__Lu 1 ‘J-..

'H fid-T‘ ‘m-«v-:‘

' "“7"". “MM" 7:"‘7' 3". . .. 1 "1 '
J'LLJLLJ‘IL 4:112‘1, U3J.-.J :u;1....ulli Del k: ¢WL

nnm nr: -«n'fiw-'rr~1 f'v-v-n Y‘x r171 1 T“. (‘1
Animuu NW3 JULuLHU Uni; CV-1¢JLJ LETLL DD

 

Per—Cent
Index of Slope Standard Error of
Product Correlation Per-Cent Estiiat
Iri3ht hoeing ‘Kright Peeing Uri3ht Seeing
Zethoc Yethod hethod Fethed *ethod lethed

 

.agnetic Tape Handler .97 .35 37.0 30.5 2.1 16.3
Table 4.6)

Data Stora3e Unit .95 .31 90.3 32.1 4.3 24.7
Table 4.20)

n —- ‘ A -". / 4“. if“, f‘ P, A
computer Component 1; .99 .do 91.9 71.9 4-4 43-1
(Table 4.25

Computer Component 53 .99 .97 35.1 30.5 3.0 8.3
(Table 4.13)

Bind ing Eachine El .99 .97 94.3 31-4 1-2 “'4
(T 331011.27 ,

Ci ndin3 hachine ”3 .97 .33 95-2 95.3 0.3 4.0
(Taole1.3j

3indin3 Lachine #9 .97 .33 91.0 92.7 1.3 6.3
(Table 4.34)

PI‘ nting Prew $2 .999 .395 33.5 37.5 0.7 1.3

(Laole 4.43)

Printing Press #7 .999 .97 91.2 90-3 0-5 4-3
(Table 4.43)

Printing Press #3 .994 .9:2 35$t 33-4 3.1 4.6

(ladle b.49)

1 CC h .
pr 58 [1‘9 .9440 0‘46 9,200 9008 201 5.3

 

 

 

 

 

 

 

-35_
the cumulative average line to be linear, produces a significantly
higher index of correlation. In two cases the difference is less than
.01 and is considered as insignificant. Which of the two methods will
produce a more reliable linear function? In each of the eleven cases
use of the Peeing method results in a standard error of estimate sig—
nificantly larger than that obtained when the Tright method is used.
It should be noted that the difference in curve characteristics is
much greater in those cases where data was available for only about
fifty units.
It is 103ical to expect a 3reater correspondence to a linear

function when the Wright method is used because the avera3irg tends

to smooth some of the assignable deviations which will be tore evident
in the case of Boeing rethod. Assi3nahle deviations may be defined

as major fluctuations in man-hour requirements which are caused by
changes in the product or errors in recording data. It is inherent
in the Uri3ht method that deviations from the straight line are
minimized. One "had" lot or unit value will have less effect on the
cumulative average than on the unit curve.

esults Conearison

 

It was stated in the preceding paragraphs that theoretical analysis
shows significant differences in results obtained when the'firight and

the Posing methods are applied to a hypothetical unit number one value.

»1

n practice when the straight line is fitted to cumulative avera3
values and unit values the theoretical unit number one value is not

the same. This is due to the fact that the least squares line is a

product of all the points plotted and not just the first unit value.

u? 01 this line of eest fit to unit number one will produce
a differe1t unit number one value do pending on wheth<r the "rig ht or
the Seeing method is used.

L341C8t88 that in terms of reliability as Ineasured eJ
the cemputed1xof correlation and the standard error of estimate,
the rright method is more desirable. Another question relative to the
two methods is: how close can actual total man—hours be predicted
through the norzvial amialication of the Jright and the Boeing method?
Accordingly, total nan—hours consumed at specific quantities were

1"

estimated. The Hri ht and the ieeing metlo:1was used to project man-
hour data. The estinates were compared :ith actual nan—hours and the
tual percentage error computed. The results may be observed in
Table 3.5.
The estimates were computed using the Wright and the Boeing method.

The linear function was used in both cases, and of course, least squares

method was BDJ1l€d to comulative averace and unit data. The forecast
11 s

‘4

{as nlade on the assumption that the applicaele slope wa sknown. M1

CD

assumption may or may not held in a specific situation.

In general, it may be stated that the'Nright method produces
more accurate results than the Foeing method. However, in most cases
both methods produce comparable results. In eight out of eleven cases
the difference in cumulative total man—hour estimating error is about
2 per—cent. Greater accuracy may be expected from the application of
the wright method. It should ee noted tlat tEe error is s 'allest in
cases where changes in the product during production were of minor

influence on man—hour consumption.

-1
O

\J \I A _

.

 

 

1 H 1 O mac no see he o_Q.He HHH
m.H O.H aOW.Om Onw.mm OO_c.mm mm 15.:
m.m H.O emm.om OQR.QO OOm.aO OHH
O.m m.O me.m\ an.Hm OOO.N OO
c.H m6 mew m: 01am. 11 83.3 on. mes;
H.O a.H Hmm.OH mmm.OH Qum.OH Om
H.H 110 mm» mmmfi OOQK O:
m.m m6 gram 31,18 013$ «OH in c
m.H a.O OOO.O1H HOO.RH OeH.nH as
mm.m O.m HHH. c NO0.0 OOH.O Om
NH m.HH Heed HOE OOO.N a 9.11
H.HH :.m om5 as wom.wm oom.mm 0m
O.H m.H sum.mm OHN. m on .mm om
NC: H.H QR 3 555.0 95.3 5H mmtn
m.HN H.e emm.\ OOH.O oaa.m Om
m.m m.O mau.m mmm.m Omm.m Om
m.m u.O eON.H meH.H mwO.H OH mm.Q
H.H m.m OH..O Osm.e mOO.e Om
3.0 N.O 0mm. 1 Omwfl.m OOmam OW
m.m ®.N md©.H 0mm.H mmm.a OH 3H.$
s.m H.m BHO.mH OOH.QH OOO.QH OOH
H.e m.m OiO.O mOe.O mum.O Om
N.mH O.O mos. mom.m mmm.m OH Ow.1
N.HH m.e manna ONH.O OOm.e ON
O.m m.H Ham m OOO.O OOO.m OH
H.N m.o mow Hmm mm H 0.3
weave; pogpe; mpsepscou PH:3 :Icm. mpso use; kpflpcdsq .0: one»
mcHoom 23%.. H33 H38 H309 -. L
epmgflpmm epmeflpmm o>apmassso e>flpmH3350 o>flpmadado
ea 1011a eH 1011M eoapo; Hazaoa season
. wcfleos MSMflLE

 

‘1) 1.; >.1,IH1JV. 4 \41- 4d:q<,1.1 H. )1! \J ._‘ 1.14“; I. )AN 4) .1 )‘Jr1 Jql‘ 1. . 1) 17

.3 pmpmmmo CO

.on magma op Hgoam>fld

m 9033:: ammo

« x: a .2.
mpmd L 523 H

.4 Epflb

 

..) u a 3
_ O O OOO OOH OOm.HOH OOH.OOH Omm
Mm o o omH.HmH 03:.oma www.mmH mom
. H m KOO m: OHH Hm OOO.OO On
> a l .
m N N m mma MHH omo.waa mfih.0HH Gum
x \ a I .a ,3 ‘
H O Q O H;p.mm mmm.OO magnum OOH
d.m m m 00H he can 03 msm mm so 0:.:
o a 2 ,
N.m H O OOO HHm HOO.OOO me.Omm HOO
m.m m.o owm.Hmm mmo.Hom mm3.mwm mmm
.. 1W. \ a mu W . d x, a
m Q c o mHm Hoc mud HHo own OHN mo: AO.Hcoov OQ.Q
:1 OOgHOH OommOH Opmop1mmw OLOOO-OOH OHOOR-OOH OHHHOOOQ .Oa OmOO
wdHoou. stHHE. Hmpoe Hagan .Hmpon
mmeHpmm mpmsflpmm m>HpmH3250 m>flwmfizfijo 9>Hpmassjo
CH pougm cw popgm weapon Hugged Uogpmg
MHCHOOHH QHHmeeHZ

 

:Oouludg MOO Humm on H<Oeoa a0 nomeam;du

-89-

Despite the large difference in results obtained when the Wright

and the Boein

C")

method is applied to an identical unit number one value,
this condition should not become a reality in practice. It was pointed
out above that the difference in projection results from the fact that
both the unit and the cumulative average lines were assumed to be
straight lines and starting out at the same point on the vertical axis.
This procedure is incorrect. When both lines are used for estimating
purposes, one of then must be integrated and this will result in that
the two lines will start at different points on the vertical axis.

The foreg in; may be proven in another manner. When a least
squares line is fitted for an actual set of data, the unit and the
cumulative average line will start out at different points on the
vertical axis. This result may be readily observed in Figure 3.7.

Another indication that the two methods will yield similar results
may be observed in Table 3.5, where a comrarison of the error in
estimate suggests that the similarity in total man-hours estimated is
Close.

It is evident that neither of the two methods of estimating man—
hours can be termed as being wrong. It may be stated that in cases
where data is available in let form, it is more convenient to use the
Uright method. Under these c nditions the unit data can only be
estimated.

A¥lethod of Unit Curve derivation

For some applications it is necessary to have an estimate of

hours expended on a specific unit. There are several methods which

may be used to obtain the unit curve when the umulative average curve

F‘;
_>o_

is known. It will be recalled that the Wright theory is based on the
hypothesis that the cumulative average man—hours per unit decline at
a constant percen age as the quantity manufactured is doubled. If
the cumulative average line is straight the unit line will be curved
for the first ten units, after that it will tend to approximate a

linear function on 105-105 paper.

Figure 3.5 presents graphical view of the relationship between

('1‘

the Uright cumulative avera e and the uni

3 curve. The hypothetical
values for the cumulative average curve were obtained from Table 3.3.
The value for the Uright unit curve may be easily obtained when the
cumulative average man-hour values at given quantities are known.
For example, assuming an 80 per—cent slope cumulative average curve
and one hundred man-hours for unit number one the cumulative average
value for unit number two will be eighty man—hours. To obtain the
unit value for unit number two we need only subtract the cumulative
total for the previous unit from the cumulative total applicable to
the specific unit number for which unit value is being determined.
To continue our example: cumulative total at unit number two is one
hundred and sixty man—hours at unit one it is one hundred hours, the
difference between the two must equal the unit value (sixty hours in

this case .

The above method was used to develop he unit curve in Figure 3.5.

:4

t is apparent thatihe'flright unit curve is curved until about ten
units are produced. Thereafter, the unit curve tends to parallel

the cumulative average line. Strictly speaking, the two curves are

not exactly parallel, even past the ten units, but the variation in

-91-
distance between the curves is small and difficult to observe. For
practical purposes the curves may be considered parallel when the unit
curve exhibits a slope which is similar to the cumulative average curve.
It was stated above that in the case of data contained in Column two,
Table 3.3, the unit curve exhibits an 80 per—cent slope characteristic
when we move from 16 to 32 units.

As a matter of practice most of the airframe firms, whose pub—
lications were reviewed in Chapter 2, state that they consider the
two curves parallel after the initial quantity where the unit line is
curved. To determine the position of the unit curve at any point in
production, a factor for each slope is multiplied by the cumulative
average cost. The factor shows relative values of unit-man-hour cost

to cumulative average man-hours. A factor may be obtained by sub-

tracting the slepe exponent from one (l—b). Since the slope exponent
for any 80 per-cent curve equals to .322, the factor will be:
l.~.322 = .678.

Applying the factor to Figure 3.5, the unit line will equal to

67.8 per—cent of the cumulative average line value at any point on the

curve. But most users of the curve realize that at the beginning the

unit line is curved and plot the first several units and thereafter
use the unit curve as though it were a straight line.

The above method is based on the following mathematical computa—

tions:
let y be the cumulative average man-hours per unit

a is the man-hours required to produce unit number one

x is the given unit number

6The 80 per—cent is obtained by dividing unit value at unit 32
by unit value at unit 16, or 32.77:u0.96=30.004 per—cent.

i92_

IV\*~—‘ /

T‘ .. ('K
~{L-4.LJA-J J. (J

-'/\-r fT vrw my? j T ”w o {—1-Tn‘ vl-1~-w-‘ ---\,~1w "1’1" MV'Y“
, . .-x . t ‘

a“ . (1,“ “I”! a, f: ‘ .. . 1 . >7
‘d‘yli\ls'~.o UL-VI._L1u"J a.--“ ngJ 'XA..L\..’..D;L_L i-‘...J'_-J..JL_J- LL-J

:fi“ “* ‘r1"‘ * if ‘Q A/‘77 ' N "TTf‘ Y“"rfi " *7 ' .
\JU‘..ULIAX.L_Lb/L A‘jfiitxi'u'q A D 1“,..1 L-..l.>. uLRufE

 

q “p 7“ ~ ‘ -- "- , L1. ,
.L i dCLuI‘ QLLOrIlILg itc‘lcxbive
. vlr' 1‘ $.’ . ‘II'\ 7"! I 0
on value 0L unit gun—”ours
L n. Y'" I‘L. _, ‘I r ,-a
to o lUldblVC Average

‘ T?
f‘ 3‘. - C) BITS

-7J-
b is the exponent which defines the slope then,
. . b
cumulative average man-“our per unit = y=ax

. b+1 b+l
total man-iour expended = ax = ax

b+l
According to the theory of integral calculus, if a formula for a
unit curve was available, and if that formula were integrated for a
given number of units, the total number of man—hours expended could
be found. The formula for cumulative total man-hours is known. Since
differential calculus is integral calculus in reverse, it is possible
to differentiate the above formula to obtain a formula for the man-

hours per unit line, or the unit man—hour time reduction curve in terms

of the cumulative average time reduction curve.

d(T) = d(ax bfil
dX

dx
. . . , b
bnit man—hours per unit = (0+1) (ax )
. b . .
ince (ax = y, we have unit man—hours per unit = (b+l) (y)

Thus the factor b+l multiplied by the cumulative average man—
hours for any unit will give the unit man—hours. In this manner a
value on one time reduction curve can be converted into a value on
the other curve by the use of the conversion factor b+l.

Table 3.6 provides a series of factors for various slope percent-
ages, which may be used to convert the cumulative average values to
unit values.
§ummany and Conclusions

In Chapter 3 theoretical considerations pertaining to the time
reduction curve were discussed. The time reduction curve theory as
originally proposed by T. P. wright is based on the hypothesis that

the cumulative average direct man—hours per unit decline by a

-9)-
constant percentage as the quantity produced is doubled. Another
formulation known as the Boeing unit average curve theory is based on
the hypothesis that the unit average man-hours per unit decline by a
constant percentage as the quantity produced is doubled.

The time reduction curve theory assumes that the established trend
of the rate of time reduction will continue, that the product is un-
changed, that the labor accession or separation rate remain the same,
and that there are no major interruptions in the production cycle.
When any of the above factors are present, serious irregularities in
the time reduction curve may be expected to appear.

Because of the difficulties in making projections of this pheno-
menon on arithmetic scales, it is seldom used for this purpose. The
man-hour data plotted on double logarithmic scale has a tendency to
correspond to a linear function. The relationship may be presented
through the use of a formulae or graphically, depending on the required
accuracy.

Application of the alternative‘Wright and Boeing theories to
actual data indicates that similar estimating results may be expected.
The minor differences are primarily due to differences in construction.
As may be expected, the wright cumulative average line is more stable
than the Boeing unit line. This is primarily due to the greater in-
fluence that individual unit values have on the unit line. However,
man-hour estimates obtained through the use of the two methods do not
indicate clear cut superiority of one method over the other.

In cases where data is available in lot form, it is desirable to

use the wright method.

-95-

The'Wright cumulative average curve method is used throughout
this stuiy. Lethod of determining the unit line when the cumulative
average curve is known is also presented.

In Chapter 4 the method of obtaining data, reliability of data,

and the data itself is presented.

0:21P. 311‘ IV
T113 . EDUCTICU CURVE DLTA
Introduction

The time reduction curve is an accepted tool of forecasting
direct man-hour requirements in the airf an: industry. It will he
recalled that most of the presentlya vailaole studie on the time
reduction curve, ”hich “ere reviewed in Chapter 2, were based on data
collected by the Air Force through periodic reports from the airframe
manufacturers.

It should not be assumed that the application of the time
reduction curve to the planning of Operations will be reutzal on the
observed data. The ti re reduction curve is used as a 3 sis for set-
ting prices, cost targets, nan—hour re: Muiret1en s, leadtime, and
delivery schedules. is in the case of other techn cues of planning,

once corn itzents have been r

p.

ace, management will do its best to live
up to these. If perations turn out to be as the time reduction
curve based plan intended, there is no comp ulsion to ta (e remedial
action. On the other hand, when experierce beg in s to deviate from
the time reduction curve, management goes all out to find and elimi—
nate the causes of deviation.

In order that a number of important (uestions relative the use—
fulness of the time reduction curve may as ansuered, it appeared

des iraele to analyze man- hour data experienced in procuction situa—

tions which have not used a time reduction curve.

-96-

 

 

-377-

The three firms which consented to release man-hour data, did
so only after being assured that the company's name and product's
trade name will not be revealed. The information was obtained
through personal examination of the firms' records and interviews
with management personnel.
hethod of Obtaining Data

Twelve manufacturing concerns were approached to obtain man—
hour data on specific products as the cumulative quantity manufac-
tured increased. Seven of the firms approached refused to release
actual data, stating that the data is of highly confidential nature.
Two of the firms denying use of data, agreed to let the writer
examine the man-hour figures on the firms' premises in the presence
of a management representative. It may be added that a definite
reduction in man—hours, as cumulative quantity produced increases,
was observed. to statements can be made relative other character-
istics of the time reduction curve, since there was no opportunity
to compute these. As an example, one production executive who agreed
to consider the request for data, wrote the following:

I am afraid I am not in position to give you

the kind of information you would really like, namely

actual man—hour production cost changing at a constant

rate as experience is gained. The reason I cannot

give you the information is the fact that it must be

considered confidential both relative to my current and

past connections. I know it does not help to say this

learning curve is factual (for thesis purposes) with—

out substantiating data, but I am not in a position to

disclose operating data.

Two firms were willing to make man-hour data available, but

Upon extensive reviews it became obvious that it would be economically

 

4;-
impossible to get accurate data. This was due to the fact that the
firms' accounting procedures did not report man—hours in either unit
or lot form. An attempt to refer to individual operator time sheets
did not produce satisfactory results. Ion—availability of time records
was one of the difficulties encountered.
Nature of Jan—Hour Zeta

The selection of a firm for study purposes is a serious problem
in itself. This is because of the fact that many operating procedures
used by a number of firms are not conducive to the time reduction
phenomena nor to the collection of time reduction data. To begin
with, firms which operate under an incentive piece rate for wag
payments or control purposes are likely to create an environment
which is conducive to restriction of output and inaccuracy of time
recording. Thus, some of the firms which were initially contacted
could not be used in this study because operating standards are set,
and the worker is paid on the basis of the percentage of standard
reached in performing a given task. During the investigation it
also came to the attention of the writer that once the standard is
reached, the workers tend to do other activities than those which
are normally associated with production. In one instance the stan-
dard would be reached Friday morning, the rest of the day workers
would engage in non~productive activities. Further inquiry into the
behavior of production workers who work on tasks where standards were
established, indicates that restriction of output is not an uncommon
case. Another frequent occurrence is the inaccuracy of time record—

ing where either standards or piece work wage payment plan is in

_,7_
effect. Again the time that the units were produced is not necessarily
the time that it is to the advantage of the worker to report on the
time sheet.

The other major difficulty was a result of the type of accounting
system used. The type of system in use not only affects the avail-
ability of data in the form desired for the purposes of time reduction
curve research, but also the data is often found in aggregate form
which defies ex post analysis. It is probably true that most of
these difficulties can be overcome with a great deal of time and
effort. In one case it was estimated that it would take a year to
come up with the cost applicable to a certain product. It is with
these possible difficulties in mind that the writer approached the
problem of obtaining empirical data on production time reduction.

In all cases we have accepted the firms' accounting definition
of direct man-hours, and have used the data in the form it was found
in company files. There was little opportunity to adjust the data
for changes introduced when the units were in production. This would
certainly be most desirable. Unfortunately, none of the firms in
question keep a cost history which would enable us to know the
magnitude of change in terms of requirements of man-hours or the date
and the unit number the change was incorporated.

Data Reliability

At this point it may be well to consider some of the differences
in the three firms methods of accumulating the man-hour data. This
is not intended to be an exhaustive or complete examination of the

firm's accounting system; our purpose is to indicate what are

-100-

considered to be important peculiarities in the system that have a
bearing on the accuracy of the data.

_§cmpany A is a leading manufacturer pf business machines. The
net sales for 1958, amount to over half a billion dollars. The
company's electronic work started in 1953, when it received a con-
tract for small computers and related items. This work came to an
end when the customer placed the business with a competitor. Placing
the data processing system into production was the most extensive
product development project ever undertaken by the company. Company
A employs a standard cost system throughout its production facilities
engaged in manufacturing a standard line of products. The electronics
assembly department is a notable exception. Here the job order cost-
ing system has been used ever since the inception of this program.
The reason for going to the job order cost system was that this work
was new to the company, and it was decided that this would be the
best way to keep track of the cost. Also, in pricing the units the
company wanted to be certain it would cover the actual cost connected
with production. Also, company officials are anxious to determine
any decreases in cost as cumulative production continues. The
company had little information on what the electronic system program
would involve as far as costs were concerned.

The job order cost system used by Company A is similar to job
order cost systems found in other situations. Briefly, when an order
is placed on a computer unit, a ledger is set up for the particular
order. The particular computer will have a unit number assigned to

it and the various operations on the unit are assigned job numbers.

 

_101-

The worker's time tickets are then posted to the particular job number
and then to the ledger. The procedure was reviewed step by step and

it doesn't seem that there is a built—in prejudice against accuracy in
the system itself. One of the interesting variations from the usual
procedure may be found in that the company charges the time of the
inspection force to direct labor. And whereas it was found that there
is very little opportunity or incentive for direct labor to charge

time improperly, in the case of inspection labor there is some reason
to believe that it may be more convenient for an inspector to charge
all of his time to one particular unit whereas, he may have worked on
three different units. This would then cause a considerable fluctuation
from one unit to the next. It should be stressed that this is only a
suspected possibility. Interviews with the department head and the
foreman did not indicate that this condition actually exists. It
should be also mentioned at this time that the practice of including
inspection labor in direct labor would seem to introduce a conservative
bias to the time requirements for the unit. There is no pressure on
the inspection labor either to complete the unit at the specified time
or to become more efficient in its work.

It should also be stressed that the direct labor data obtained
,W?$.that for assembly Operation only. Since the parts machining
labor is compiled on the basis of standard cost and not on a per unit
basis, it is impossible to trace the man_hours to the point where they
would become useful in time reduction analysis. Furthermore, the
parts which are produced by the company are produced in a department

where an incentive piece rate wage plan is used. Close to 70 per-cent

 

-102-

of the parts are procured from outside vendors, and these are charged
to material cost.~”Qata was obtained for two different programs. The
”first program covered the period from 1953 through 1957, and the data
rcqyers five computer components, one converter unit and one control
unit. The computer components were produced simultaneously as were
the control unit and the converter unit. Although these parts would
at a later date be assembled by the buyer into a unified data process-
ing system, each one of the computer components was especially de-
signed and different from the other units. The company made these to
order for one of the larger electronics manufacturers. The production
of the company's line of unified data processing system equipment
began in hay of 1958. The first shipments were made during the first
quarter of 1959.

Company B is a newcomer to the electronics manufacturing field,
having started operations only fourteen years ago. It has steadily
grown until present with sales running approximately ten million
dollars annuallV. Small electronic motors is the specialty of the
company. All of the production items are made to order.

Firm B has a modified job order cost system of accumulating time
data for fixed interval units in the total quantity produced. Thus,
the first two lots consist of five units each. Thereafter time data
is accumulated for lots of ten, and occasionally for a lot of twenty.
gnly assembly time data was obtained from firm B, because close to
30 per—cent of the parts going into the assembly are procured from
outside vendors, and man—hour data for parts produced by the company

would be misleading. This is due to the fact that company B has a

 

-103-

policy of manufacturing certain parts in lot sizes greater than
assembly lots. The parts in excess of assembly needs are stored for
future assembly needs or issued as spare parts orders are received.
Only the time of direct hourly workers is charged to the assembly

hour account. The firm's output for which data was obtained consists
entirely of Specialized components used in data processing systems and
automated control systems. The manufacture of these computer compon-
ents and data storage units started in 19h9 and ended in 1951.

Company C is one of the oldest printing press and bindery machine
manufacturers. It is considered a leader in its field. Sales for the
fiscal year ending June 30, 1959, were over twenty—five million dollars.
Unlike in the case of firms A and B, where it was possibke to obtain
data only on part of the products produced, at firm C man-hour data
was obtained on all products manufactured, beginning in 1950 until
the present.

The cost system used by firm C, may best be described as a job
lot system. The company initiates the production process only after
orders are received. Normally, action on the first few purchase orders
is delayed until enough additional orders are received to make up what
is considered a sufficient number of units for the lot. Only in the
case of one model was the company known to deviate and produce a few
units at a time. It should be noted that the data obtained from this

_-""‘

manufacturer represents both assembly and machining time. In this
case, it appears to be significant because over 95 per—cent of the
parts used in assembly are manufactured by the company. (It may be

added that a large percentage of the parts are bought in the form

11;;-

of unfinished castings and then machined to specification in the
plant. Foundry work was formerly done in the plant but it was dis-
covered that castings could be bought for less than it cost the
company to make the same.)

The company redesigned its line of printing and binding equip—
ment in the early part of 1950. It seemed logical to start with this
date in obtaining time data. If the time reduction phenomenom was in
existence it would be most apparent after a significant change in the
product. New products added since 1950 were picked up at the time that
man—hour data became available, and, of course, dropped when the product
was discontinued. Only one printing press, the production of which
began in 1950, is still being produced and continuous data was obtained.

Whenever possible, the data used in this study has been checked
for accuracy and completeness. In a number of instances, the depart—
mental data, as recorded when the operation is completed, was compared
with payroll data for the same period and showed no discrepancies.
Furthermore, it is judged that, since the workers or the timekeepers
do not have an incentive to be biased in either direction or toward
Specific units, any unintentional errors will offset one another.
All observations are reported in spite of the fact that greater con-
sistency would be obtained, had a selection been made.

pata obtained from firm A may be found in Tables 4.1 through
‘4114. It will be noted that this data consists of two programs.
Tables 4.1 through 4.6 cover man—hours expended in the manufacture of

an electronic data processing system, and was available on a per unit

basis. To obtain a common basis of analysis cumulative average

m-_.d-— ,

-105-

man-hours per unit were computed and used. Kan-hour data contained
in Tables 4.7 through 4.14, represents small computer components and
one control unit. The data was obtained in totals for quantities
produced. Data in Tables 4.15 through 4.26 was obtained from firm B
and was in lot average form. Cumulative average man—hours per unit
were computed and may be found in the last column of each Table.
Tables 4.27 through 4.54 represent firm C man-hour data experienced

in the manufacture of bindery and printing equipment.

lfifi

n. zl~

r5}

.l. W/L.

A. a!» {1 IF»

7«

r‘

J lid a...

 

-106-

TABLE 4.1
DIRECT l‘Z'TI‘IEIOURS PER UNIT
CONTROL UI‘VIIT NO. 2

 

C Uf-IIIAT IVE C UjfULrtT IVE
11mm 3 TmuL mmmnEIimmms
UNIT NO. PER UNIT KEITHIOURS PER Uj-IIT
1 1,137.8 1,137.8 1,137.8
2 578.7 1,716.5 858.3
3 517.6 2,234.1 744.7
‘* 493-1 2,727.2 681.8
5 1+25.2 3,152.4 630.5
TRBLE 4.2
InmmTTammmnlmRumn
HIGH SPEED PRINTER no. 1
1 3,089.8 3,089.8 3,089.8
2 2,022.6 5,112.4 2,566.2
3 1,962.9 7,075.3 2,358.3
4 1,857.9 0,933.2 2,233.3
5 1,274.5 10,207.7 2,041.5
6 1,195.2 11,402.9 1,900.4
7 1,134.5 12,537.4 1,791.0
8 1,134.8 13,672.2 1,709.0
9 1,066.0 14,738.2 1,637.5
10 1,004.7 15,742.9 1,574.3
11 988.7 16,731.6 1,521.0
TABLE 4.3
DIRECT HLNHOURS PER UNIT
HIGH SREE PRINTER E0. 2
1 1,580.4 1,580.4 1,580.4
2 1,506.1 3,086.5 1,543.2
3 1,341.6 4,428.1 1,476.0
4 1,314.9 5,743.0 1,435.7
5 1,211.0 6,954.0 1,390.8
6 1,166.0 8,120.0 1,353.3
7 1,222.9 9,342.9 1,334.7
8 1,185.8 10,528.7 1,316.0
9 1,278.4 11,807.1 1,311.9
10 1,201.8 13,008.9 1,300.9
TABIE 4.4
DIRECT :uuaoDRs PER UNIT
CIRD REIDER UNIT E0. 1
l 1 4 0.4 1,470.4 1,470 4
2 ’934.1 2,444.5 1,222-3
3 926.7 3,371.2 1,123.7
4 595.8 3,967.0 991.

-107-

Till-ELIE [4’05
DIRECT 732117.101le PER UNIT
TAPE PERFORLLTICII UI-IIT NO. 1

 

cm 1'01sz IVE CUT-UL'EIVE
‘ :1 3m OURS T OTAL IVEIuCE 212.313100'Rs
IIUT N0. PER UIIT ‘RWHOURS PER UNIT
1 630.8 630.8 630.8
2 560.4 1,191.2 595.5
3 642.4 1,833.6 611.2
4 548.4 2,382.0 595.5
5 472.5 2,85’+-5 570.9
6 511.9 3,366.4 561.1
TABLE 4.6
DIRECT InEHOURs PER UNIT
IECPETIC TAPE UEIT NO. 1

1 620.7 620.7 620.7
2 493.5 1,114.2 557.1
3 338.4 1,452.6 484.2
4 479.4 1,932.0 433.0
5 292.4 2,224.4 444.6
6 369.1 2,593.5 432-3
7 274.4 29867-9 409’?
8 310.8 3,178.7 397°3
9 412.0 3,590.7 399-0
10 359.0 3,949.7 394.9
11 330.3 4,280.0 339-1
12 239.8 4.519-8 376°7
13 253.4 4,773.2 367-2
14 358.9 5.132-1 366°6
15 339.5 5,471.6 36”
16 292.9 5,764.5 360°3
17 264.6 6,029-1 354.7
18 218.4 6,247.5 347-1
19 248.6 6,496-1 341.9
20 181.9 6.678-0 333'9
21 225.3 6.903-3 328'7
22 217.1 7,120-4 323°7

—lO8-

TJPIBIJB LL07
DIRECT I‘lz’iffiT-IOURS DATJ‘I
COT-ITROL UT-IIT N O. 1.1

 

cm RELATIVE CUTRJIET IVE
,. TOTAL IVER-«10E xix-moms
LOT :10. UNITS tau-moms PER UI‘IIT
1 1—5 ’ 659 137
2 6-10 1,091 109
3 11-20 1,731 87
4 21-30 2,289 76
5 31-37 2,601 70
TABLE 4.8
DIRECT I-RLETOUR DATA
COE~TUTER NO. 1.4
1 1-5 749 152
2 6-10 1,430 143
3 11-2 2,918 146
4 21-30 4,350 145
5 31-39 5.558 142
TABLE 4.9
DIRECT FTAEIHOUR DITA
coz-IJUTER NO. 2;.
1 0-5 1,210 242
2 6-10 2,328 233
3 11-20 4.355 218
4 21-30 6,200 207
5 31-40 .947 199
TIBLE 4.10
DIRECT ZEALIHOURS DATA
co:E>UTER 110. 3.4
1 1-5 3,085 617
2 6-10 4.971 497
3 11-20 7,218 36}
4 21-30 8,980 299

-109-

TRBLE 4.11
DIRECT FREHOUR DflTA
CQPWHTML kl

 

cm-TJLIT IVE CUE-L'UL'LT IVE
TmmL ImmuCE imbue
LOT NO. UEITs EEUEOURS PER UTIT
1 1-5 3,233 647
2 6-10 5,681 568
3 11-20 9,640 544
4 21-30 12,316 410
TTBLE 4.12
DIRECT TuUUOUR DATA
Cdeummim. 5A
1 1-5 6,243 1,249
2 6-10 9,917 ~92
3 11-15 12,578 839
4 16—23 15.384 668
TABLE 4.13
DIRECT EIUBOUR DITA
CORPUTER U0. 6i
1 , 1-5 8,234 1.647
2 6-10 13,338 1.334
3 11-20 19,167 958
4 21-30 24,054 802
TABLE 4.14
DIRECT MANHOUR DITA
C0:-T>UTER :10. 7;.
1 1-5 4,744 949
2 6-10 8.992 899
3 11-15 13.416 82“
4 16-20 17.626 891
5 21-30 25,937 864
6 31-38 32,119 845

NOTE: Data Contained in Table 4.1 through 4.14 obtained from
Company A.

-llO-

T513133 4.15
DIRECT .iil-UTOUR DATE-‘1
COIVPUTER NO. 213*

 

0.anme

oo-Qmmc‘th—J

Lm' cumnnnm CUDDTDE
AVERAGE TOTAL AVERAGE JRHHOURS
UNITS MANHOURS IAHHOURS PER UTIT
1 1-5 604 3,020 604
2 6-10 670 6,370 637
3 11-20 157 7,940 397
4 21-30 169 9,630 321
5 31.40 164 11,270 282
6 41-60 165 16,140 269
7 61-70 157 17.710 253
8 71-80 153 19,240 241
9 81—90 139 20,630 229
TABLE 4.16

DIRECT HUMOUR DATA
COI-PUTER NO. BB

1-5 232 1,160 232

6-10 212 2,220 222

11-20 197 4,190 210

21-30 153 5,720 191

31-40 150 7,220 181

41-60 123 9,680 161
TiBLE 4.17

D IRECT ZIQpIIOUR DAT};
CO::'PUTER NO. 43

1-5 381 1.905 381
6-10 300 3,405 341
11-20 322 6,625 331
21—30 257 9.195 307
31.40 210 4,295 282
41-50 192 13,215 264
51-60 176 14.975 250
61-70 147 16,445 234

Data contained in Table 4.15 through 4.26 obtained from
Company B.

—111-

T113113 4.18
DIRECT I-IQHIOUR D-’=.T11
COITUTER ITO. 5B

 

LOP cmanTws mnmumrn:
tm‘ ,, “TREE -TmlL . Immmmznmpms
1.0. U.. ITS 114731- 103718 3111.330? ,5 PER TJEIIT

1 1-5 183 915 183
2 6'10 123 1.530 153
3 11-20 123 2,760 138
4 21-30 109 3.850 128
6 31-40 79 4,640 116
7 111-50 74 5,300 108
8 51-60 69 6,070 101
9 61-70 67 6,740 96
10 61-70
TRBLE 4.19

DRntTIEUmRRIITA

COHPUTER 00. 6B
1 1-5 208 1,040 208
2 6-10 102 1,850 185
3 11-20 148 3,330 167
4 21-30 172 5,050 168
5 31.40 116 6,210 155
6 41-50 98 7,190 144
7 51-60 86 8,050 34
8 61-70 72 8,770 125

TABLE 4.20
DIRECT :LTEOUR DITA
DATA STORAGE UHIT E0. 18

1 1-5 247 1,235 247
2 6-10 232 2,395 240
3 11-20 198 4,375 219
4 21-30 194 6,315 211
5 31.40 170 8,015 200
6 41-50 159 9,605 122
7 51-60 174 11,345 1:
8 61-70 165 12,995 05
9 71-80 139 14,385 180
10 81-90 89 15,275 170
11 91-100 86 16,135 101
12 101-110 74 15,875 153

 

 

an 1 IL

-112-

TABLE 4.21
DIRECT ZRHHOUR DATA
DATA STORAGE UNIT NO. 23

 

Iflr Imf~5 Gumnmnm cmmmmnm
RWRQL TmuL Ammmm:ummms
»0. UNITS :LIRROURS IRHHOURS PER UNIT
1 1-5 206 1,030 206
2 6-10 99 1,525 153
3 11-20 98 2,505 125
4 21-30 121 3,715 124
5 31.40 77 4,485 112
6 41-50 70 5,185 104
TABLE 4.22
DIRECT :ERROUR DATA
DR 1 STORAGE URIT R0. 3B
1 1-5 128 640 128
2 6-10 124 1,260 126
3 11-20 70 1,960 98
4 21-30 82 2,780 93
5 31-40 62 3,400 85
6 41-50 63 4,030 81
TABLE 4.23
011130 1271.;1IHOUR D.2T;.
COPmEREd 7B
1 1-5 550 2,500 550
2 6-10 374 4,370 43
3 11-20 304 7,410 371
4 21-30 180 9,210 307
5 31-40 164 10,850 271
6 41-50 149 12.340 247
7 51-60 113 13.470 225
8 61-70 107 14,540 208
T4813 4.24
DIRECT TREEOUR DATA
COI-TUTER :10. 83
1 1-5 176 880 176
2 6-10 161 1,685 169
3 11-20 108 2,765 138
4 21-30 130 4.065 136
5 31.40 98 5,045 126
6 41-50 99 6,035 121
7 51-60 79 6,825 11"

 

IL.

//
r

-113-

TIIKBL-E [+025
DIRECT l-E’TIITIOUR DATE.
COIITROL UI-IIT ISO. 13

 

1%“)? ggbiiTl'VE V“CzUr-IUIRTIVE
.1 1.: ~‘. 1.: b1.» ‘ 13 A E 113:0 n
UXITS KITTOURB ILYHCURS h ngR U?:T URD
1 1-5 110 550 110
2 6-10 123 1,165 117
3 11-20 73 1,895 95
4 21-30 78 2,675 89
5 31-40 51 3,185 80
6 41-50 54 3.725 75
7 51-60 63 4,355 73
8 61-70 48 4,835 69
9 71-80 29 5,125 64
TABLE 4.26
DIRECT :RRROUR DATA
CO PUTER R0. 18
1 1-5 482 2,410 482
2 6-10 338 4,100 410
3 11-20 251 6,610 331
4 21-30 30 9,660 322
5 31.40 23 12,000 300
6 41-60 203 16,060 268
7 61-70 162 17,680 253
TABLE 4.27
DIRECT 33.11::10111 DATE;
BEERTG:RCELRJTO.I_
1 0-10 990 9,900 990
2 11-13 810 12,330 948
3 14-19 697 16.512 867
4 19-23 662 19.160 833
5 24-30 650 23,710 790
6 31-36 537 26.932 743
7 37-51 502 34,462 676
8 52-56 488 36.902 659
IDLE 4.28
DIRECT TERROURB DATA
BLIRUG:ICRIRJUO.2
1 0-1 509 509 509
2 2-4 518 2.063 516
3 5-12 448 5,647 471
4 13-17 395 7.622 443
5

18-25 357 10,478 419

-1l4-

TLDLE 4.29
DIRECT ILHHOURS DATA
BIRDIRIIRCIIEI:RL 3

 

um cumnnIn: CUDDRDE
TOT. 1 . ..mmmmE TmuL Inmmmrummms
NO. UNITS unnROURs tLEEOURS PER UNIT
1 0-7 605 4,235 605
2 8-11 612 6,683 608
3 12-16 507 9,218 576
4 17-23 468 12,494 543
5 24-27 421 14,178 525
TIBLE 4.30
DIRECT :RTROURS DRTR
BITDLIIIRCEITT KL 4
1 0-2 800 1,600 800
2 3-3 702 2,302 767
3 4-4 668 2.970 743
4 5—5 545 3.515 703
5 6-8 472 4,931 616
TRBIE 4.31
DIRECT :RRHOUR DATA
TIRED D :RCHITE E0. 6
1 0-6 262 1.572 262
2 7-10 205 2.392 239
3 11-18 198 3,976 221
4 19-28 182 5,796 207
5 29-37 171 7.335 198
TABLE 4.32
DIRECT 117128101011 DELTA
BIRDING IRCRLIE 1'10. 7
1 0-6 335 2,010 335
2 16 276 4.770 228
3 24 245 6.730 290
4 32 251 8.738 273
5 41 236 10.862 265

 

 

-115-

TABLE 4.33
DIImCT ii"...:"-E";-IOEH1 D.".T.71
BITFDII'IG :RCE-IILE NO. 8

 

‘ TOT cmDLnuma MEUDIDm
LOT _. .1: ERIGE . . V TOTAL .1VER’.GE TIREIOURS
rm. Uins IUHWRS rumpus E3 RET

1 1-9 289 2,601 289
2 10-17 270 4,761 280
3 18-22 275 6,136 279
4 23-30 277 8,352 278
5 31-39 238 10,494 269
6 40-48 243 12,681 264
7 49-57 242 14,859 261
8 58-66 248 17,091 259
TIBLE 4.34
DIRECT TEEROUR DATA
BINDING IRCBIRE R0. 9
1 0-16 216 3,456 216
2 17-29 177 5.757 199
3 30.40 165 7,572 189
4 41-48 163 8,876 185
5 49-57 183 10,523 184
TIBIE 4.35
DERECT 331311101111 DELTA
BIRDIRG RICHIRE R0. 10
1 0-12 223 2.676 223
2 18-18 183 3,774 210
3 19-25 172 4.978 199
4 26-39 169 7.344 188
5 40-50 182 9.346 187
TABLE 4.36
DIRECT EITEOUR DATA
BINDING IICRIRE To. 11
1 0-2 302 604 302
2 3-13 257 3.413 263
3 14-25 235 6,251 250
4 26-33 227 8 . 067 244
5 31.4.3 215 10 , 217 238

-116-

TIE-LE 4.37
DEECT :RI-IROLR BITE
BIZIDII‘EG IRCIIIIIE :10. 12

 

LOT C U? CULZT IVE C UTIJIAT IVE
138E ' ' UNITS ”“303 1917;} AVERAGE TRITOURS
° 4“ rnstURS ihAflOURS PER UYTT
1 0-3 2’3 759 253
2 4-4 202 961 240
3 5'8 194 1.737 217
4 9-15 176 2,969 19,3
5 16-22 164 4, 117 187
TREE 4.38
DIRECT 1T. 1.1-TOUR DITI
BIZ‘IDIE-IG E‘L'TICHIEE 110. 13C
1 0-12 592 7 , 104 592
2 13—42 306 16,284 388
3 43-72 305 25.434 353
4 73-102 295 34,284 336
TABLE .39
DIRECT 3312-1101111 DATA
BIRDING l-IC‘II E 1:0. 14C
1 0-10 547 5.470 547
2 11-25 456 12,310 492
3 26-40 365 17,785 445
4 41-55 334 22.79 414
5 56-70 330 27.745 326
6 71-85 320 32.545 303
T1813 4.40
DIRECT ITIUROUR DATA
BIRDING IL". HIEE IO. 15
1 0-20 467.0 9.340 467
2 21-40 356.0 16,460 412
3 41-70 282 24,920 356

ri~

:10

 

-117-

T.‘--.:3LE “2.2421
DIRECT ITII'KIOUR DEITII.
BINDING I‘L‘lCUIZ‘E NO. 16

 

Lm? CRDLnIna CUmRRTns
Lm‘ #8868 nmu. Inmxmzammmn
NO. UNITS RRNTCURS EIITOURS PER UIIT
1 0-20 385 7.700 385
2 21-40 310 13,900 348
3 41-60 244 18,780 313
4 61-80 213 23,040 288
5 81-100 175 26,540 265
6 101-120 169 29,920 249
TI'LBLE 145.1452
DIRECT IIRROUR DATA
PRITTIRG PRESS NO. 1
1 0-5 2.550 12.750 2.550
2 6-15 1,730 30,050 2,000
4 16-30 1,385 50,825 1,694
5 31-45 1,175 68,450 1,521
6 46-60 1,099 84.935 1,416
T BLE 4.43
DIREC LRRUOUR DATA
PRI:ITI:~IG PRESS 1.10. 2
1 0.10 1,170 11,700 1,170
2 11-30 890 29,500 983
3 31-50 752 44,540 891
4 51-70 685 58,240 832
5 71-90 70 71,640 796
6 91-110 655 84.740 770
TI'IBLE 115.4145
DIRECT TERI UR DATA
PRIRTIRG PRESS NO. 3
1 0-10 1,275 12.750 1,275
2 11-20 1,065 23.400 19170
3 21-35 850 36,150 1.033
4 36-50 770 47.700 974
5 51-65 755 59.025 298
6 66-80 735 70.950 “76

P

41“—

!» .l «v by

 

-118-

TABLE 4.45
DIRECT 3113310011 DATA
PRIE-‘ITII-IG PRESS 1‘30. 4

 

LOI‘ C UT-TUUIT IVE C [H'fLTII’IT IVE
L01 AVER‘IGE TOT-51L EVER; E 331311100118
NO. UNITS f‘-1-‘;P"IOURS 1211.33101le PER UZI IT
1 0-10 1,295 12,950 1,295
2 11-35 902 35,500 1,014
3 36-60 716 53.400 890
4 61-85 625 69,025 812
5 86-110 510 81,775 743
6 111-135 514 94,625 701
T1818 4.46

DIRECT 214 21.780011 DITA

FRII'ETIIVIG PRESS ISO. 5
1 0.4 965 3,860 965
2 5-14 893 12.790 913
3 15-34 674 26,270 773
4 35-54 619 38.650 716
5 55-74 647 51.590 697
6 75-94 589 63.370 674

TABLE 4.47

DIRECT 1111-1310011 DRTR

PRILFI‘IIIIG PRESS BIO. 6
1 0-5 2,625 13.125 2.625
2 6-15 1,878 31,905 2,127
3 16-30 1,580 55,605 1.854
4 31-50 1,414 83,885 1,678
5 51-70 1,232 108.525 1,550
6 71-90 1.152 131.565 1,461

 

wu/ 1n.

A

-119-

DIRECT 211121710011 DAT}.
PRII'ITIIEG PRESS HO. 7

 

um cmmu11n: cumnmrmz
mm 1211 1-1 1wmxm .1muL mmamgzzxmwa
10. 01113 711110085 x1310URs PER 0111
1 1-10 832 8,320 832
2 11-30 694 22,200 740
3 31-55 618 37,650 684
4 56-85 565 54,600 642
5 86-111 524 68,224 615
6 112—140 498 82,666 590
7 141-167 491 95,923 574
8 168-195 503 110,007 564
9 196-225 503 125,097 556
10 226-253 502 139,153 550
11 254-283 515 154,603 546
12 284-313 496 169,483 541
13 314-343 462 183,343 535
14 344-373 474 197,563 530
15 374.403 463 211,453 525
16 404.433 415 223.903 517
17 434.463 410 236,203 510
18 464.493 412 248,563 504
19 494-523 417 261,073 “79
20 524-553 411 273,403 “9“
21 554-581 406 284,771 490
22 582-611 400 296,771 486
23 612-641 395 308.621 “31
24 642-671 410 320.921 478
11318 4.49
DIRECT 3118001 0111
29131110 PRESS :0. 8

1 0-6 962 5,772 962
2 7-16 734 13,112 820
3 17-36 601 25.192 698
4 37-66 503 40,222 609
5 67-96 435 53,272 555
6 97-136 368 67,992 500
7 137—186 328 34,392 #54
8 187-236 322 100,492 42
9 237—286 330 116,992 “09

 

 

 

 

-120_

 

8L3 4. 50
088011 48811
PRINTING PRESS 110. 9
ME 088L888 0888888
181 UERCE TUML 97948-51m88
NO. UNITS H1880URS :118088S PER 8:11 __
1 0-10 845 8,450 845
2 11-20 782 16,270 814
3 21-40 638 29,030 726
4 41-70 552 51,110 730
5 71-90 580 62,710 697
6 91-115 556 76,610 666
7 116-145 562 93,470 645
8 146-175 565 110,420 631
9 176-205 534 126,440 617
10 206-235 529 142,310 606
11 236-255 494 152,190 597
12 256-270 462 159,120 589
13 271-285 448 165,840 582
14 286-295 475 170, 590 578
15 296-305 480175.390 575
16 306-315 459 179 .55 9‘30 571
17 316-327 464 18 5, 548 567
18 328-339 496 191,500 565
11818 4. 51
DTRECT‘, 12088 D 11
PRIHTIHG PRESS NO. 10
1 0-10 611 6,110 611
2 11-20 546 11, 570 579
3 21-35 516 19,310 552
4 36-50 486 26,600 632
5 51-60 520 31,800 530
6 61-80 506 41,920 524
7 81-100 499 51,900 519
8 101-120 492 61,740 515
9 121-150 468 75,780 505
10 151-168 469 84,222 501

-121-

DIRECT IL'LIHIOUR DATA
PRIIII‘II-IG PRESS NO. 11

 

um 0118188 0118188
L01 . 1 88108 1011L 1788108 111800 9
10 LNHB 331113 :11018 P11181
1 0—8 1,275 10,200 1,275
2 9-12 1,124 14,696 1,225
3 13-39 966 32,004 15069
4 31-43 826 42,822 996
5 44—57 791 53.896 946
6 58-72 768 65,416 909
7 73—86 893 77,070 896
8 87-103 764 90,066 874
9 104-122 898 107,128 878
10 123-140 958 124,372 88
1 141-156 817 137,444 881
12 157—171 884 150,704 88
11818 4.53
0111801 11101008 0111
P81311110 PRESS :10. 12
1 0-5 1,927 9.635 15927
2 6-7 1,484 12,603 1,800
3 8—18 1,269 25,562 1,476
4 19-20 1,111 28,784 1,439
5 21_27 1,017 35,903 1,330
6 28-33 »82 41,795 1,267
7 34-38 953 46,560 1,225
8 39-39 971 47,531 1.219
9 40.42 887 50-192 1,195
10 43-43 931 51.123 1.189
11 44-45 974 53,071 15179
12 46.49 855 56,491 1,153
"BIBLE 4.54
DIRECT Illffi-IOUFé DAT}.
8110110 LLCHIHE 10. 5
1 0-5 679 3,39 679
2 6-8 58 5,138 642
3 9—10 564 6,266 627
4 11-13 554 7,928 610
5 14-16 468 9,332 583
6 17-18 432 10,196 566
7 19-21 33 11,494 547
I'IOI‘E: Data contained in Tables 4.27 through 4.54 was obtained from

Company C .

Summar*
One of the serious difficulties encountered, during the process
of gathering empirical man-hour data, was the reluctance of firms to

release such data. Even after consent to release data was obtained

it was found that in some cases the firm's accounting system did not

report data in the desirable form.

Historical direct man—hour data consumed at various cumulative
quantities of output was obtained from three manufacturers. The

data represents five production programs of a total of fifty-four
products. These fifty—four products were produced in various quanti—
ties, ranging from seven to about one thousand units. There was also

a considerable difference in the total production time for the products.

The period covered by the five programs varies as to the date and

also the duration, ranging from 1949 until July of 1959. The program
duration ranges between two years for computer components, to about

ten years for a printing press. Three programs represent production

of various data processing system components. The other two are

bindery equipment and printing presses.

The firms' methods of man—hour recording were reviewed in detail
and departures from standard practice were noted. All three firms
use a variation of the job cost system. The review did not indicate
the presence of incentives to biased recording of time. Whenever
possible, the data used in this study were checked for accuracy. Ho
discrepancies were discovered.

"Analysis of data contained in Tables 4.1 through 4.54 will be

found in Chapters 5 and 6.

RELliBILITY OF THE TIHE REDUCTIOH CURVE

Introduction

It will be recalled that in Chapter 1 it was stated that the

objective of this study is to determine whether or not the time

reduction function, as proposed by wright, is a reliable tool of fore—

casting direct man—hour requirements. The following specific questions

Jere posed:

1.

Does the time reduction curve phenomenon exist in manufacturing
situations other than those where production activities are
based on a planned time reduction function? No assumptions
were made relative to the effect that such use of a precon—
ceived time reduction model will have on observed man-hour
data. On the other hand, it should not be assumed that the

use of a time reduction model for the purpose of budgeting

and controlling man—hours will be neutral on manufacturing
time requirements. Therefore, it appeared desirable to analyze
empirical data observed in situations where the time reduction
curve is not used for purposes of budgeting and controlling of
man-hour requirements.

The second question, which will be considered in this chapter,
concerns the reliability of the linear function of the time

reduction curve on log—log scales. An attempt will also be

-124-
made to determine the reasons for deviations from the straight
line on double logarithmic scale.

The above order of analysis will be used for the balance of this
chapter.
Pattern of Time Reduction

A time reduction curve was computed for each of the fifty—four
products. There can be little argument as to whether the slope is
positive or negative. In each of the fifty—four cases for which data
were analyzed the time reduction curve had a significantly negative
slope. The question whether the time reduction curve phenomenon exists
in manufacturing situations where a curve is not used for planning
purposes may be answered in the affirmative. It has been suggested
that the belief and the use of the curve in planning is responsible for
the existence of this phenomenon.
The Linearity of the Curve

It is the purpose of this section to evaluate the reliability of
the time reduction curve in its linear form. An index of correlation
for the fifty—four products was computed. The index of correlation is
identical to ordinary correlation coefficient except that the former
term is applicable to curvilinear correlation. The index of correla—
tion for each product will be found in Column three of Tables 5.1
through 5.5. An average was also computed for each program and is
shown at the bottom of each Table. In support of the linearity pro-
position, it may be stated that all but one of the fifty-four

empirical time reduction functions computed resulted in a close

 

'A““‘—v~

.4

v -* .1 ‘

C:

‘.. ‘, , . ‘ _.
L);.~..lxl~-‘.L-..L-.J ”54.; ‘.--\r"J._JuV-'-.-.u

‘-

‘l‘ <

i “k- ' J—uLJ

-4. x).

J i

-125-

J’OJ.

‘I ‘ ‘ a
—-5 $-J-0-AJ--—A—v-L—LJJ

'Y

:Jnv44-

~JK.-.J. b”

.JA.L~)

 

-_ ’ “X I 1'"
J ‘ ‘ x
l - -L"~J---.‘. .nL O 4., J- —L. -_ at
J—ou-..J.‘-- a.)
‘ . w _.' ‘3
.3.....1‘-_J‘u 4.4.'...L_.'- Val-1
1 V ‘1 “. .‘ , ‘ t '
A .4“ v.4..i L-‘ HJLii-~.i..J
. " ,‘ ru’. I ' i . fl ' I ‘ f- Y I“ \
H . .1 « ‘ I\, }
A..k.;..‘ u- u .L .4 J» .1.....-...\.i. ‘Ji \J‘;l-\./)
4'3‘ ~+ Y‘ 1 - ‘7‘ o L- r. ,r '. j l f, _-
' I . | ,v .‘ ' . . ‘ ,I "
DVALU; O-A- L'-L_LU ;:O. 5.4 “’ 0‘ 0 /, / -O‘—j
if: ‘ 1‘ L“ ,‘L'V-V" F. ‘.'I- "‘L ‘ -«'| ~'( 7“ “ .1. I A P "—;'
L&.L.LJ$X .‘gi/V'Jul lLLilLin “Jo kg...- -" 0//'v 1-0.év
_. ‘. , . . J ‘ . A k ,‘ .e, y, Q /
.V —r _,~,. v-< '.‘ r- , .
-‘i.\_,1-l .Jiz._,Ukl l J. lflbLl -.Uo w ,‘/o f o /' 7’ 4.0
—"I."l “(‘11,)V‘ ‘( l 'I. ‘ 1‘ ' r) l
u(.-i(4 -ct,!}.¢1_‘,l aux). ‘JLYOV' ° /‘//') I“.
r" r) " ‘ 1n ‘VI‘E‘ 34 r~ ' «4 “ a "I '1 1' ‘, ‘l
-ui/‘C‘ fpi i 9.101 ,'." o o ‘,'.2 4.0‘?
_ I F. _, ‘ ‘ 1
'. -"-‘P'-1 I .7; .~, ' ‘ ., “ ' -‘
l—;-‘ ALL, Ll-l-C -L. )b Vial [(4 LR.) L‘ J v 0 K . 1 / \‘I “‘."’/

{\i

-126-

r~.-'~ .1 n

1 I
-.£—"L~J / 04:,

shin-QC C” 3. ft. C. CI‘BXLQKCTEILISTICS
Sig-ECLLOIJIC COMPUTEJS

‘ -
‘ - H I ' l / ' l ..
l -rLr'~—J»~“A—~- ..\10 L. L‘L.¢- 4.

,‘W‘. ‘ "“

ui.x..un-LJJ

”'7'." " ,‘ '. ’ 01‘

.J—a.J.J..JJL A- ¢‘\-UA.- A

;~'w r\ ‘1 'r‘. f‘.';1 ll“, - '. '- ,-- ‘\

lily v.1-.‘i U1. Au AiaLLH

.. .. . V ‘
.3 Ja—mr‘r'! ,‘1 flaw , ,.‘,\ ,‘ , r1" - , - . 1‘
‘ ‘ f I. - .-. . "i i .7 .

“ “'L'-J‘-"V JLL'; .‘J JL‘.‘-J._‘1L¢LL.LL'-. ( .-&,[ CL?! 1 U2

n v'. - r \r w. ‘.
uOI’ltr’Ol unlt In (P/ . .4. . /)/,2 J . g;
r“ .__ ‘ 4» w‘ a I. I) r) -

\JO. .&)J—"J£)l M lj\).!_/ O I/,/|\) _1_ 'x)?’

t

“ C“)
O.
”:2
t;
Cf“
(D
“S
N
.' r.-
C;
\-
0
x.
L
K.
[__J
t_.‘
K-

LYLC'Y‘ r: 2:. , ’ C) v‘,"
d4..\) Ll .L /“k ‘1}. I” ./’ ) ~.\,/
" '\ -/ -1 iv.
”n ‘7" Q L‘ , ‘ - \ x ,
\JO nLJJgU .4)" 4X \ j . ’ . / ‘1 I . ~\’
"1 w“ 4- , .1 ‘ w ,\ 3-1 L" x
VO _’:_ib 3]“ :h‘. T‘J‘). \J 9 'II/ J. JQJKJ
:V‘V \ 7., _ r‘ r, I \ ‘( l' u
v . Ml E21" 6“ .2304” .t/ I) ZO'JL
h I. z
. "l' "A\ 7" ‘ > ‘
V0 ‘ J‘lter Ki}. )Ido) o IJLi’ a 2K)
P P fl >’ .a . [l .' I‘ r
,.\ r " L. L. ’
auJJx Clpe ‘J/O/ ./ Y‘.) j. j )

'1
)

‘ 1“", “m
~- 'JL \JL

J

'r.

(1 _,\ .L
oer-puter
-‘ -
CC.
T‘O ,. . J. i
\J .11.“..1U:
VOCLCL'.
A
f‘ .\
VO 1.
q
UO.1:)‘
" .1- .
vO.,..)dbCr
('\ ‘. J-
VO. lpUL/er

C,"\ k!" {-2, \a) P.)

v-

! \.

C

o
" .1!., r‘

‘C: - 1
I; ‘3 Vi Cap-k;

storage
I lrx Ad- , "‘ ‘L . '
dbv‘uC-‘L t4 {JOI‘C'LUB

~ \ I“ ‘1. .V
UC. Ucl

ah, i
‘J'l LI(.A.

1",— ‘f-l' f
N) b0]. LA-QAJ

.J

‘

"a“; "fif‘fi

J.)

pnit
tuiit

in

r" ‘

r'--

‘ '- 3 A ‘1 :v‘,
U‘Ja‘ LL4‘L..A. LA 1 O

.A.-
h'

inbu luv-g .L

1 1 ,
auL A—r‘
’7 1'
L. i.’

V' . f) ‘

i t j i.

a m, -3 i ‘_-,.‘_.-- -
v ixxlr. £.v-L.u-'Ju.-).L-.U

- .-

-127...

fit- “.1 l); 5 o 3

a 'vw ~ “\1"“.'_“ '- “’fi' ”‘1
.-o v. u.-:x-|-‘-vi..1.._L.J.L_A_\/J
”fl‘Ar‘JV

ob. .i’ti. i. . -

“ ~ >"“ ‘
Q-_.JL.41-

‘ w -

7' ’2 w“ _ .
I.L\.«‘u~-‘.£i ...LJ. J, .L-La.¢'. .J

.L. \‘j~J‘L

“."z {1"fi‘ ' 1 ("A '0
H « ‘ l U i
A x4... JAJ.Il x

~--\--s u 1"“ .».
I I P . l
.J..-\. i .4 '

,'|: ‘
qv- -_ .-L.'1iugi .-- v-

P‘ ‘ f,“ 7’
I
\JLI/O / . / / )
Vp" '-'h’
, _. n ,/
1’ IV . ‘ 0 / I C
w _.»‘r’
L \ ._,.- _\
' ‘k, .\’ . //J
-: .. ",- .
_,‘..i. \J . / \Jx.)
._ I .
'\-))Q l O /’ 1 U
' : V2. '9
JL} 0') . /¥AA’
l..-',’ ' J)
( o 'x x/
\ fl '3

 

.. Jr,

,, "V i, W
y‘Jo) .///
.2“

\r.) 5: j ‘
(Vl;.) o/x-IJ.

,3 my
'x /‘o -‘ . I/ Y
. '5
‘ ‘7 - UL
/\JQJ .// ‘

clung-aha)

1 ..V V r~‘ -‘
,1 , ‘ ,'1
‘J..-Ay -v A

‘1’ 0.1.

k);
0
_\s
(—

N.
W
I
\4
PO

\_I)

. I

b.—
T'

0 'V \-
"1 . ’)
J O ‘4‘ {a
fix .'\
A: 1 O ,

- 128-

..- _,_ .fi , g
‘ f-
1:1;an 'Q‘T’
- _, J
- ' ‘ - ~' “"1 1W1 l/\ _’V H ,-\r ‘a ' _ WT'I'"1 __
JU;.;-L..'_ C’L' .L o -co u. ui41-vai.J--4..J.t__\/~J

-- ‘A—ij ~v- \ - :~ fl-T‘
. . -‘ 4 , -~ \ ',
J4..-_J_J-.-L gVL-xliA-J...
7" ‘ " ' "a" I. 1’“ l K"
J . '3 - ,«i I ‘1‘ |
I-.. J.~L.- Mb. ‘7’, ....4_...m- J

.,,.,.. _.-‘, d‘

\.

.Jig.-3H'JL-‘.;J

" 7"" "‘ " "‘- a”; CC
’ ' i.e./2.1.x .4- -..~.\J-. -

4.1.4.3.J_..

.- ,,_-_ , 1...
C ” "‘U" "" CWT 7 0‘11”” L Ii w. .‘ :3 ‘44

x-.u-“.i-._‘; .‘J.- via-Ht a .J-J~-s-¢ -
a . _. . -.-._ ‘L

v-—- -- ._. V... ,~‘~\—-‘ fir -. ‘ <1 ‘ . v ‘x 74 .g. v1

‘ . . . . ‘ L -. [
I UQLAJ.’ ub.r.--_1.....-.L~.«-a -\.- pup

 

"I ,‘\/ .
_11‘ 14‘ a‘ \ ‘_. _‘ l
l \4‘ r gt) 0 , / .2 v
1 ,‘ /- 4 ,' f.
‘v ‘lt-J.L O'~—UJ jo/
/\
,\ a / (‘f\ r’ r_ "
N \’ I . ‘54 I
j /'*C‘ V ' //D A” ’-
I"\ f
3' ”v; ‘ . '1 H)
“r \J{o‘J ., ,/ V'J
W ’ x)

C . Kn
\
c
O

(”1.3
O

\O\O\O
O\HQ
O 0 0

PH
C;
U1

3—
I

\O
H
.
U\ COKH C) N C) F—5 \C:
C
\

H
F-

'I- \O \C ‘ _:
4:-

1/‘\ 'V\ ,,
.v‘ ,
.y U. . I / I
‘ l ' O
I V
. . .. o
‘"/) I102/O ,‘ O 4 J\)
‘ H ”"2 ' ‘1, r-‘_",
L‘ " ' .l... ’1‘
— " in) . J O 1 , - J
.1 ;\ / . ‘ 31. a
'5 i " ’ o O

H w
(p
o

1"V‘r r ‘r "f f L C ' .
AvCl’EL ,53 ».J/./\J 0/(1
k)

 

d ‘__J_1

JV......'.-._‘.

\ "‘1 (Y1
i J. - o

‘.... na-

r-w . ’r -~‘

A. ‘ 1,.»

-o.

-v~.

lJiux.L .1—-.|\J

I"
'J C

‘V' " ‘ “F" ‘1 .5'."‘v'1" "
u -L.‘L J.._Jlt_..._/i +~Jq

.—3 -

1 V .
t.) . . . -.
i . “4.4;: .4.)

E-.C?d--1;- -'.C. 5, FI-d-i C

,‘I.‘ __ . ‘7
I

‘1'»- -- -..J..J-.-.:

'1 \ . ,. "1

‘ 1
54--...(JA'4 kl-
‘_ "' ‘ '| \
AJJ—LMAX‘J

{ -.~- _ -_'.\
\ .. C_..-uj

 

f4

\
I

«'2' K») C

.,
\

(Mk)

I

l
O O
3 Kit \-

(a
I
\-

g} {I o \1

,1 r)

".1. o I...
a” 'I
$.“.’

"J

.n

4 1‘

/‘(., o \z

‘-/' \
‘VI‘ :4"
. / z‘ /

' —l

‘ I
' I / /
~\ ‘I v
° /( I
<

'I

, ,h’

. z / '
r "/
.l \Jl
‘ilf'Vlt‘
. / / II
., .

. I/ /' /
V/ '

‘ ,1-
. / / '

’/
I':
.41
2
‘,4 "

fw \r“,
. \,
/ ' /' /

O

I .
A; o "J
.

 

9‘

 

.I
..._j_ jg}.—

approximation of linearity. The straight line was computed through
the use of the usual least squares method. In fifty—one out of
fifty—four cases the index of correlation was greater than .90. In
one instance the correlation index was .738. The average index for
all products is .95. The average index for the various electronic
data processing system components is .972, the range for (program
No. l) the six components being between .890 and .998. Program No.
2 experienced the lowest correlation, the average being .9k6, and a
range between .738 and .996. Program No. 3, Firm B, consisted of
eight computer components, three data storage units, and one control
unit. The correlation average for computer components is .967, with
a range of .911 and .995 the average index for data storage units is
.954. The average index for the sixteen bindery units is .977, with
a range of .868 and .999 at extremes. The twelve printing press
models exhibit an average index of .990, and a range of .967 and .999.
Evidently, the index of correlation is higher than one would
conclude merely from observation of the actual time reduction curves
(Figures @.1 through 4.23). On the basis of above analysis, we may
conclude that actual time reduction curve data when plotted on double
logarithmic scale tends to exhibit essentially a linear function.
Despite the high index of correlation to a straight line that
is exhibited by data, a visual examination of the various time re-
duction curves found in Figures 4.1 through 4.23 indicates that there
are numerous deviations from a straight line, which would, at those

specific points, introduce serious error to our estimate. (Figures

4.1 through 4.23 may be found in the Appendix).

 

-131-

Departures from linearigy

It is possible to have a relatively high index of correlation
and yet find individual values to deviate widely from the straight
line. Simple visual observation of time reduction curve derived
from the plotting of actual data does not enable us to make any
precise statements relative the reliability of the function. The
important question that may be asked here is: with what degree of
confidence may estimates be based on the linear form of the time
reduction curve? In cases where the relationship between two
variables is perfect, all of the plotted values for individual pro-
duct units would fall on the line of regression. If such were the
case, the regression line equation could be used as an exact tool for
predicting the value of one variable from a given value of the other.

In most real life situations the values for the individual units
do not fall on the straight line, and the relationship is not perfect
This latter case is certainly true of data for all products analyzed
in this study. Under these circumstances, when the linear equation
is used to estimate the man—hours per unit at a given cumulative
quantity, the man—hour figure becomes only an estimate which is
indicative of the average relationship between the two variables.
Before this average relationship may be used in prediction with
confidence, a value measuring the reliability of the average relation-
ship and the concentration of the values about the least squares line

must be computed.

The standard error of estimate is a statistical tool which

provides a measure of reliability and concentration of values about

 

-132-

the regression line. The standard error of estimate is similar to
standard deviation except that the former deals specifically with
curvlinear relationship, and values are developed through the use of
logarithms. Hereafter, the standard error of estimate will be
expressed as "S". Given an approximately normal distribution of
points about the line of regression, the following statements may be
made: (1) About sixty-eight cases out of one hundred will fall about
the line within plus or minus 18. (2) Ninety-five cases out of one
hundred will fall within plus or minus 25. (3) And 99.7 cases out of
one hundred, will fall about the line within plus or minus 35. If an
estimate of an aggregate value of man—hours is desired for a given
quantity of production, the estimated line of regression may be used
with confidence. The actual value may not be on the regression line
but in 99.7 out of one hundred cases, it will be within the limits
of 38. It is evident that the standard error of estimate (5) affords
a measure of reliability of basing estimates on a line of regression.
Because the time reduction curves were computed by means of
logarithms, the S is also expressed in terms of logarithms. Since
the standard error is difficult to interpret in this form, we have
computed actual percentage values. The S for each of the fifty-four
products will be found in Tables 5.1 through 5.5, column b. It
should be stated that the percentage error values are for 13 only.

To obtain percentage values for 23 and 35 we need only to multiply

 

1A detailed description of the statistical methods used in this
study may be found in F. E. Croxton and D. J. Cowden, Applied General
Statistics, (New York: Prentice-Hall, Inc., 1940), Chapter 23.

 

-133-

the value given by the number of S desired. The standard error of
estimate percentage value is identical at any cumulative quantity,
and is directly related to the least squares line fitted to actual
data. It represents a constant ratio, in percentage terms, of the
top line to the average line, and the average line to the lower line
(-13).

Obviously, a fitted average line with a small standard error of
estimate is more reliable than one with a large S. The average S for
programs one and two, experienced by firm A, are 2 and 3 per—cent
respectively. These deviations are considered small and the line is
reliable for estimating purposes. Tirm 3 time reduction curves
exhibit a larger S. In only three cases in ten, is the S larger
than five per-cent. However, the data storage units have a high per—
centage S, the average being about seven per-cent, which is due largely
to a twelve per—cent error in unit 33 data. The average S for program
30. 3, computer component data is b.20 per—cent, the highest being
for unit 23 which amounts to nine per-cent.

The lowest 8 percentage was experienced by firm C, for bindery
equipment and printing presses. For the twenty-eight products on
which data was obtained from firm C, in ten cases the S from the
least squares line is less than one per-cent. The S average for
binding machine is 1.65 per—cent, while for printing presses it
amounts to 1.73 per—cent (Table 5.4 and 5.5).

Before any conclusions relative the reliability of the time
reduction curve in prediction can be made, we must first make a

decision as to what percentage of S will be considered as reliable.

-131+-

The accuracy necessary in a specific case depends on the use to which
the estimate will be put. For the purpose of this investigation, an
arbitrary limit of S of 4 per-cent magnitude was chosen. It is
believed that S of less than 4 per—cent will provide sufficient
accuracy for many purposes. Of the fifty—four lines of regression
computed in only nine cases does the S percentage exceed this arbi-
tary test of reliability. It should be noted that in six out of nine
cases the reliability is of some usefulness because the S is less
than 5 per-cent.

It is concluded that within certain confidence limits (4 per—cent)
actual data tend to correspond to a linear function on log—log scale.
Test of reliability of the linear function, as measured by the index
of correlation and the standard error of estimate, indicates that
the relationship is reliable.

Some Reasons for Departures from Linearity

While the industry average data may be useful for comparative
purposes, in order to use the time reduction curve in specific situa-
tions, it becom s necessary to analyze the time reduction curve for
individual models within individual production facilities. In Chapter
3, it is stated that the relationship between cumulative average man—
hours required per unit and cumulative unit number will tend to
exhibit a straight line on logarithmic paper. Unfortunately, the
real situation is quite different from theory. It would be an unusual

case if actual production was predicted with a great deal of accuracy.
If this were the case, it would mean that the time reduction curve has
anticipated all the possible factors that might arise to interfere

with the expected course of events.

_-

. h-m

-135-

Usually, as a production program is put into effect and as
actual direct man—hour data becomes available, deviations from the
initial estimate of the time reduction curve are likely to appear.
This should be expected since individual time reduction curves will
usually reflect the individual factors that influence a specific
production program. A visual examination of Figures 4.1 through
4.23 indicates that in a number of instances the deviations from the
line are considerable. In many of the cases under consideration, the
data approximates the linear function remarkably well.

It seems appropriate that an analysis be made of the possible
causative factors responsible for the deviations. A conference was
held with the department head concerned, cost analyst, and a foreman
in order that the deviations be discussed. There was a general agree-
ment that one of he most important factors responsible for deviations
from linearity was the numerous engineering changes introduced while
the units were in production. (The problem of engineering changes
will be discussed in detail in Chapter 3). A large number of engin—
eering changes of varying magnitude have been incorporated into the
various units produced by firms A and 3. Unfortunately, neither the
additional man-hours required nor the time of incorporation can now
be reconstructed, since many of the changes are effected without a
change in blueprints, and in some cases, it takes a year to bring
the latter up to date.

The second important deviation causing factor seems to be due to
qualitative failures of parts and assemblies. It should be noted that

this situation arises as a result of lack of proven design of the

-136-

components and assemblies. A great amount of pressure was applied
by top management of the company to be the first one on the market
with a data processing system. As one company official put it:

‘de had to give our sales force something to talk about."

Thus, as soon as the product left the research department, it went to
design engineering where it was designed with top priority. Another
rather unique situation existing in Company A, that may well add to
the problem, lies in that the company has no production engineering
department. Therefore, when assembly problems arise, as they are
likely to on a new unit, they have to be solved by the assembly
technicians. It is reasonable to expect that production or process
engineering would foresee, and solve some of the problems arising in
assembly.

A close examination of the qualitative failures reveals the
following conditions to exist in firms A and B: (1) Over 70 per—cent
of the parts going into the assembly are furnished by vendors over
which the firms have no direct quality control. (2) Some of the
parts received from vendors do not fit, and additional machining
operations are performed. This time is charged as direct assembly
labor, whereas, actually, it belongs to machining labor. In cases
where a significant amount of this type of labor is expended, it
should introduce a conservative bias into the time reduction curve
for that unit. (3) Certain parts do not function when received in
the assembly department. Unfortunately, because of the newness of
the sub-assembly, it takes an excessive amount of time to determine
whether or not it functions properly. The optical instrument going

into one of the assemblies is a case in point. It took about two

_137-
days to discover that the instrument was not Operating properly. A
few more weeks were required to return the instrument to vendor for
repair and rework. (4) Often the assembly upon reaching one of the
several inspection points will not function properly, and even after
the problem is discovered it takes time to make the necessary adjust-
ments.

Any of the above factors, wnen present interfere with the normal
progress of time reduction. Even though the workers are kept busy at
other tasks, the management feels that these interruptions cause the
workers to be engaged inefficiently. Finally, it should be remembered
that errors in time recording, in spite of the absence of a biased
direction, will cause considerable dispersion below and above the
time reduction curve.

A question may well be raised at this time whether the absence
of factors disturbing normal progress would eliminate the serious
deviations from linearity? The present data do not warrant any
definite conclusions on this point. However, the time reduction
curves on units which had a minimum of the disruptive factors to
contend with show a remarkably linear pattern (see Figures 4.1,
4.12, Q.l@, 4.17). It would, therefore, appear that a significantly
better fit would be obtained if the technology were at a level which
would permit interruption free assembly. Had this been a product
where the state of the art were such that most of the construction
problems had been overcome, it would be reasonable to expect a much
Closer approximation of a straight line. The data for firm C tends

to support this indication. The manufacture of printing presses and

 

-138-

binding machinery may be considered relatively standard. At least
there have been no revolutionary changes for decades. Some engin—
eering changes are incorporated while the unit is in production, but
these are infrequent and most often do not affect man-hour requirements
significantly.

It would appear on the basis of this analysis, that even though
in Specific instances deviations are significant, these are mainly
a result of voluntary action on the part of management. In general,
the time reduction may be closely approximated by a negatively
accelerated linear function. The deviations will be greatest in
those cases where technology has not reached a state of know—how
necessary for uninterrupted production.

It would be desirable in the analysis of linearity of the time
reduction curve to ascertain which of the major deviations from
linearity are assignable to a change which was subject to managerial
control. It would then be necessary to establish the amount of work
added or deleted as a result of this change. The data should then
be adjusted for the change, and any additional deviations might be
termed unassignable, and therefore, most difficult to predict. It
would not necessarily mean that the unassignable fluctuation is also
unpredictable. It would probably mean that our knowledge of the
fluctuation was such that we had no reason to expect the factor which
has caused the deviation to be present. At any rate, it is impossible
to make the assignable fluctuations adjustments in the present data
for a number of reasons already stated above. Since there were a

number of significant assignable changes in the products studied,

 

-139-

it appears that failure to adjust the data would introduce a negative
bias to the index of correlation and the standard error of estimate.
Summary and Conclusions

In this chapter empirical data was analyzed to obtain some
evidence to several questions relative the time reduction curve
phenomenon.

Empirical data was obtained from three midwest manufacturers.
The data represents the direct man-hours consumed in the manufacture
of fifty-four products and five distinct production programs.

Certain data generated by the airframe industry is also used to
ascertain consistency of the relationships.

Despite the many difficulties and unsolved problems, it appears
that some positive conclusions can be drawn.

First, empirical evidence strongly indicates that the existence
of time reduction curve phenomenon is not predicated on the use of a
planned time r duction function. The firms, from whom data were
obtained did not employ he time reduction curve for the purposes
of planning operations. A time reduction curve was computed for
each of the fifty-four products. In each case the regression line
had a significantly negative slope.

Second, empirical man—hour data when plotted on double log-
arithmic scales tends to evidence an essentially linear function.
In addition, it was determined that the linear function is reliable,
within stated confidence limits, for the purpose of estimating man—
hours. In all but three cases the data plotted on doucle logarithmic

scales resulted in a close approximation of a straight line. The

 

-lhO-

average index of curvilinear correlation for all fifty-four cases is
greater than .95. The standard error of estimate was used as a
measure of reliability. It was found that in 9% per-cent of the cases,
estimates based on the linear form of the time reduction are highly

.ll

.3

A

reliable (less than 4 per—cent standrrd error of estimate). The sm
standard error of estimate indicates that there is a high degree of
concentration of values about the computed line.

In a number of cases significant deviations from the straight
line were observed. Analysis of these deviations indicates that most
of them are assignable to changes in the product and in some cases to
low level of technical knowledge. It was found that in situations
where product changes and component failure was relatively absent,
deviations from the straight line are minor.

The next chapter is devoted to an analysis of slope uniformity of
the empirical time reduction curve, as well as to problems of fore-
casting slope for the purpose of projecting nan—hours to be consumed

in production.

 

CHAPTER VI
ESTILATI C THE RATE OF TIXE REDUCTIOH
Introduction

The slope characteristic of the time reduction curve is of prime
importance to the users of this tool. Slope, as defined in the time
reduction curve usage, determines the rate of time reduction as
additional units of a product are manufactured. Thus, the steeper the
slope of the time reduction curve, the greater will be the time reduc—
tion between doubled quantities. Even more important is the question
whether or not there is sufficient uniformity in the rate of time
reduction experienced by a firm so that this typical rate may be used
in forecasting man—hour requirements of future production.

The purpose of this chapter is to determine the magnitude of
variation in the rate of time reduction for the following situations:
Several firms manufacturing similar products, non-similar products
manufactured by one firm, and also various models of a basic product
type manufacture by one firm. For the purpose of this analysis
similar products are defined as those products whose function and
construction are basically the same, even though they may be produced
by different firms. For example, all models of 3-24 bomber aircraft
are considered similar to each other. A printing press is considered

as a basic product type although there may be a number of models of

this type product.

-lfil-

 

L;_.

Another task of this chapter is to explore the possibility of
estimating the rate of time reduction on the basis of man—hour data
obtained after an initial quantity of units have been produced. Yan-
hour estimates based on the forecasted rate of time reduction will be
made, and the resulting error will be indicated.

It must be recognized that failure to predict the rate of time
reduction places a serious limitation on the usefulness of the time
reduction curve for the purposes of forecasting direct man—hours
required in a production program. however, the potential gains from
projections after a limited quantity has been produced should not be

overlooked.

Uniformity in Slope

The percentage slope of the time reduction curves for fifty—four
products was computed. In each case the least squares method of fit—
ting the straight line was used. This method is more laborious but
is considered more accurate than the simple observation method frequently
used in practical applications.

The computed slope characteristics for each of the fifty-four
products are given in Tables 5.1 through 5.5 of Chapter 5. The slope
for each of the five production programs will be considered separately.
There is no reason to expect uniformity in slope for the data process—
ing equipment because the design and the function of the various units
may be considered to be different.

The percentage slope for program ore ranges from 77.7 to 97.6.

In program two (firm A), which consists of various computer components,

he production process is similar in that all direct work may

 

01".

be classified as being concerned with electronic precision work. inc
eight computer components are different to the extent that each unit
is designed to perform a function in an automated system. The varia—
tion in the percentage slope of program two units ranges from 75.4 to
96.5 per—cent.

A somewhat greater regularity of slope was experienced by firm

.1

T The dispersion from the averaye of 35.1 per—cent is not as large,

the range being between 34.9 and 90.6 per—cent, resulting in a slepe
variation of about 6 per—cent.

The time reduction curve slope experienced by firm C, on pro—
grams four and five shows a surprising amount of irregularity. The
slope range for bindery equipment (Table 5.4) is from 32.9 to 96.2
per-cent, or a variation of 13.3 per-cent at extreme points. The
rangefbr printing machines is a little smaller, being between Ch.9
and 95.4 per—cent, with about a 10 per—cent interval. It appears
that for most situations the error in the man-hour forecast, which
would result from a 5 per—cent error in choosing the proper SlOpe,
would be of such magnitude as to make the man-hour prediction highly
unreliable. The wide ranges in the slope of similar products indicates
that the possibility of an error greater than 5 per—cent is large.

A Boeing study of World Ear ll airframe production man—hours
indicates that significant variation in the slope of the time reduction

curve may be expected.

 

Boeing Document Io. 12331, (Wichita, Kansas: The Boeing Airplane
Company, n.d.).

-144-

Analysis of world War II production experience of a number of
firms shows that the average slope of time reduction for all firms

and models was 79.8 per-cent. However, the time reduction curve

slopes for individual airframes of the same period varied from 65 to
98 per—cent. The individual time reduction curves for the various
models and facilities are shown in Table 5.6.

TABLE 5.6*

PERCENTAGE SLOPE F TYPICAL WORLD U‘R II TIEE REDUCTION CURVES

Boeing;flichita (first 900 B—29's) 71.86
Boeing4Nichita (last 800 B-29's) 69.5
Boeing—Benton (first 400 3-29'5) 80.5
Boeing—Benton (last 700 B—29's) 79.0
Lockheed—Burbank (9—17) 65.3
Douglas-Long Beach (first 1000 B—l7's) 77.4
Convair—Forth North (first 1000 3-24D's) 76.4
Douglas—Tulsa (3243) 75.0
Ford4Uillow Run (3—24) 70.8
North American-Dallas (3-24) 75.0
Beech—Wichita (AT—10) 76.7
Korth American—Dallas (AT—6) 93.0
Republic—Farmingdale (P-4Z:) 39.0

 

*SOURCE: Boeing Document Ho. 12381, The Boeing Airplane Company,
Il‘irj.C}1i‘tla , (find. )0

Table 5.6 shows that a different slope was experienced in the
following cases: (1) For airframe types that were different. (2) For
different models of the same types of airframe. (3) For the same model
airframe produced by the same company at different plants (3—29'5 pro—
duced by Boeing). (4) The same model airframe produced in the same
plant (B—29's at Boeing) at various cumulative quantities.

This study and the above study of Norl ‘War 11 production by
Boeing indicate that considerable variation in the percentage slope

may be expected in several categories.

-145-

First, there is a wide range of variation in the percentage slope
among firms manufacturing either similar or identical products. Com—
parison of electronic data computer components manufactured by firms
A and 3 shows that slepe varies from 77.7 to 97.6 per-cent. A question
relative the extent of similarity may be raised in the case of pro-
ducts manufactured by firms A and B. On the other hand, even when the
product is identical a considerable variation in slope was experienced.
Table 5.6 shows that the four firms producing the 3-24 bombers exper-
ienced a time reduction curve slope range of 70 to 76 per—cent. In
the production of 3-17 bombers Douglas experienced a curve slope of
77.4 per—cent as compared to 65.3 per—cent experienced by Lockheed.

Second, analysis of data obtained from firms A and C indicates
that the variations in the percentage slope for programs within a firm
are extensive. In each case the range in variation is over 10 per—cent.

Third, there appears to be significant variation in the percentage
slope experienced by a firm manufacturing several models of a product
type. The difference in slope for the sixteen models of bindery
machines manufactured by firm C is 13 per—cent between the lowest and
the highest experienced time reduction curve. The range in curve
Slope characteristics for the twelve printing press units is from 34.9
to 95.4 per-cent. In view of the size of the variation in the slope
of time reduction curve for various models of a product type, it is
concluded that there are serious limitations in applying the slope
experienced in the manufacture of a given product to the forecasting
of man—hours of future models of the same product.

In general, it may be stated that the time reduction curve slope

tends to vary among firms manufacturing similar products, among

-la6_

products manufactured by a firm, and also various models of a basic
type of product manufactured by a firm. The variation in slope of
historical time reduction curves is so large as to preclude the use
of experienced slope in forecasting of man—hour requirements of sub-
sequent models of a product. It must not be assumed that slope which
was experienced in the past is of no value. Hhere the accuracy needed
is less than 5 per-cent, and where extensive knowledge of slope de-
terminants exists, a firm may find it useful to make projections
along experienced slope despite the dangers of error. Under these
circumstances the question may well be not how accurate does the
time reduction curve predict, but how well does it predict as compared
to an alternative method.

Next, a method of forecasting the time reduction curve slope
will be discussed.
A hethod of Slope Prediction

The time reduction curve slope is highly irregular and
therefore unpredictable in the required accuracy range.

It may be possible to obtain an indication of slope early
after production data on a certain number of units has become avail—
able. In practice the slope for following units to be produced is
often projected on the basis of several units produced.

Uhen a firm wishes to forecast the slope of the time reduction
curve to be used in projection of man—hours required in production it
is necessary to determine how many units of a product must be produced

before the percentage SIOpe oi specified accuracy may be predicted.

-147-

It is logical that the number of units which must be plotted

before a prediction of slope can be made, is a function of: (l) The

index of correlation of data to the line of regression. (2) The

required accuracy in the percentage slope. (3) The actual error

which will be tolerated in any given situation. given the preceding,

an equation may be used to obtain the number of units which must be

plotted before lepe can be predicted

Let N be the number of observations we need. Let r be the value

of the index of correlation coefficient. Let t, . be the t value

“-4.
corresponding to nzf-Z for a given alpha (say alpha 2 .05 for example).
Let e be the per-cent slope error which is acceptable. Then the

2
solution for H may be obtained in the following equation:

sv ts.
A = “-2 = fie) (r)

As an example, this method is applied to a case where six units

were plotted and an index of correlation (r) is .98. Assume that it

is required that alpha (confidence limit) equal .05, i.e. 95 per—cent

confidence of results is required. Assume that the actual error in

slope which will be tolerated is equal to .10.

t (.05)
Then, "-3 = (.10) {.93) = 49?

Referring to the t—table (may be found in most statistics texts)

for 5 per-cent confidence the n which approximates .Q92 may be obtained

as follows:

 

For proof that the equation is correct the reader is referred
to J. F. Kenny and E. S. Keeping, lathematics of Statistics, (2d ed.
rev.; Sew York: Van Nostrand, 1951), p. 210.

-43..
Try n 8 N—2 -=18 in t-table, then

t18(’05) a 2.101 = .h95 which is approximately

0
oh92. Hence, N = 18 + 2 - 20. Thus, 20 is the required number of
observations that are needed before curve slope, of above confidence
limits, can be estimated.

It is evident from the preceding example that the greater the
required accuracy the larger number of units (M) will have to be
plotted before slope can be predicted. When using this method it is
advisable to report,man-hour data on a per unit or small lot basis,
because in cases where the man-hour data is reported and plotted on a
lot basis, the quantity produced may be so large as to negate any
benefit derived from the use of the curve. The usefulness of the
above method is questionable when the number of units to be manu-
factured is small, and when the index of correlation is lower than .95.

There are two assumptions which must be made before the validity
of the above method can be accepted. 'We must assume that the items
for which slope prediction is being made are essentially the same as
those on the basis of which the slope is being predicted, and also
that the basic circumstances of manufacturing are unchanged.

It appears that the reliability of the time reduction curve for

forecasting purposes depends on how many points are needed before slope

can be predicted. If fifty per-cent of the total to be produced is

~- - v ~ ~ + pasul
necessary, the beneiits derived from the use 01 the curve are dououi

at least. 0n the other hand, our data indicates that the slope trend

-1a9-
is established and may be observed relatively early. Whether or not
it is worthwhile to use the curve in a given case, must be answered in
the context of a specific situation.

The isolation and analysis of factors which affect the slope is
beyond the scope of this study. For a discussion of some general
factors, which are judged to have an important influence on the time
reduction curve, the reader is referred to Chapter 7. Slope is pro-
bably a result of the unique production function which may differ
among firms of a given industry, as well as for various products manu-
factured by a single firm.

Estimating from Initial Quantiti

The foregoing analysis indicates that at present it is not
possible to estimate the rate of time reduction applicable to future
manufacturing on the basis of past experience. There is another
alternative available to a firm faced with the problem of forecasting
direct man-hour requirements. It may be possible to estimate the slope
of the time reduction curve on the basis of data which becomes avail-
able after an initial quantity of a product is manufactured.

Following is a brief description of the method used to estimate
the slope. Cumulative average man-hours per unit were plotted on
double logarithmic scales. It appeared logical that a greater number
of man-hour values will have to be plotted in those cases where the
deviations from the straight line are pronounced. Accordingly, at
first only three values were plotted. If the three values approxi-
mated a straight line, these values were used to estimate the slope

to be used for projecting man-hour requirements of follow-on production.

-150-

T . x "W h, n , , , . .
if it bCCame apparent, througn Observation, that one of the three

Q,

plotted values showe a pronounced deviation from the straight line
another two points were added and a total of five values were used in
estimating slope. Of the twenty—eight cases for which computations
were made, three values were used in twenty—two cases, four values
were used in three cases, and five values were used in three cases.
The results of the analysis mav be ooserved in Table 6.1. Column
1

one shows the case number, which in turn corresponds to tnc Table

A

number in Chapter h, where the original data may be found. Column two
shows the percentage slope which was estimated on the basis of the
number of man-hour values given in column three. Pecause most of the
data were available on a lot basis, column four gives the number of
units that are included in the number of lots shown in column three.
It will be noted that in the first three cases (Table 6.1) the data
was available on a unit basis and the unit values were used directly.
In each case the estimated slope characteristic pertains to the
line of best fit computed on the basis of the values reported in column
three and four. The straight line of best fit was computed through the
use of the least squares method. The actual slope for the production
run is shown in column five. The error in slope estimate is given in
column six. There is a tend ncy to underestimate the steepness of
the line when the latter is being estimated on the basis of a limited
quantity of units. In twenty—one of the twenty-eight cases the slope
was underestimated, in six cases the slope was overestimated, and

in one case the estimated and the actual were identical. The largest

difference between the actual and the estimated amounts to h.3 per-cent.

-151-

e.g- aHH mHH He
m.m- QNH NNH as H.o+ e.mH om m m.eu aw.a
m.m- new mom on
m.o- new mmm om o.:- m.au ow m n.3m mm.a
u. cm+ mmH mmH OHH

m.¢H+ OHH maH om
a.m+ mmH eaH on m.e+ m.om on m m.ac om.e
o.mH+ «3 oaH on

.m+ :aH QJH om H.H+ a. on on m o.am OH.¢
0.0m- we on on
o.mm- eoH in om m.m+ H.mm om m e.mo ma.a
0.:w dmw mow on
m.m+ sow mam om m.a+ e.mn on : o.mo NH
«.0- Hem mmw om
m.m+ mam jam on e.H+ 0.5a on a N.ea mH.a
m.m+ 3mm ma cm 0.0 n.0m m u a. an 0.:
m.©+ Hom.H we .H OH
m.m+ mam.H mH:.H a m.m+ m.mm m - 0.0m m.:

H.m| Hmm GHQ m m.HI m.mm m n

 

3.05 H.:
Haemlpem Hchnpod HHCDupmm MMHpcmmw wheQILOQ pceoumem mon eQOHm Hcouupem .ou
oneHHmm mpzorucmg mpdowlcma epqugmm ::m CH epmsHpmm oQOHm memo
CH ommmo>¢ ommme>< eCOHm :H COHpozbopm mHHcp op beameHHmm
pommm m>HpmHsESQ o>HpmHse:o poppm pom eQOHm mo .oz pom: mHoH
Hanged eemeHbmm Hmzpod mo .0:

 

LL?

SOHHQDDPi WAHH b0 Hudm 0&4 tLQ:I.fi. .mmedfiHHMfl .m> Hdzgofi ho fioo+i£mfiao

4 . 3 11.1%.-

 

I III Illa! '1 I I I

 

 

m.iw+ anwb
.J.M+ KOO
#.HH+ HOB
0.0+ m3
H.m+ may
O.m+ mom
m.H+ own
W.H+ 00m
o.HH+ new
- Nesquf. AZ)
2 C»\
mu
. H.Hfi NM
mo . \\
1 H+ ace
o.mH- om
m.H+ one
H.H+ jam
b.m+ nub
o.m+ pen

.H: com

0 [\
+
(“N
l!\
N

H.NH+ so
m.:+ mm

llr

mm

om
om

H00-

m.m+

(b

‘L_f\
C"\

.‘j '

C)

r)
K .
[\..

('\

C‘\

i

m

(N
C\
C\

mam

\ .
o.~w

OOQNI.

(C

$.H0
H.aa
a; a ONJ
’\ \ “1.

«J. 3
r. if.

m.aa

f.

 

Hzeouped Hamnubom
0 £4 1111'. a by
HmEszb mesomICma
CH ommpe><
poaam m>HpmH3Edo

Haaaoa

QHCDILODH
mm5031me
mmmbe>¢
o>HHmHSEso
eepqéHHmd

HQHHcmzé

pceoubom
mmeHbmm
eQOHm CH

gonna

,mJTOJ I

P ,

44)\/.II \) 4

25m

cpooeHao.E
pom QQOHm

Hasbvd

J.1fi\.4~.~,
. Pfr a...

eQOHm
eemEHHmm
op
mpoq
.on

pseoupom
QQOHm
UOHQEHHQ.

F»

1

-153-

:«H
m.H

5H. H
OHH. H

Ham
new

eom
mHm

\)\\
...‘ 4r.
f\.l\\L

Hmb

+5.:
OHHJ

HHm
9%

mmeuH
0mm;

0:
CC

HNH

Qdu
CC

0 he
Cfiwv
r*r4

U\Cj\
(DON
(\lm

sea
09

\Q

(“r—i
Oc¥

”F
‘3‘

——\_
"x‘

Q
‘0
r l

(\3

O
r—l
C\

o.mm

ON

U\

UN

 

 

(L.

CH

av mCLlLOnm
mhjowmlcflwa ..

HmSHO<

WQL®><

UOPmFflpmm

\Jw4~/\n,lu|\/ 4
___ r. ....
4(1Crx .xrr‘r.»

@HmfiHHmH

OOOHm 2H

Haifa «#200 l

H.C

\14 W
+C.C

‘
(»

Low mQOHm
Hezbom

\. 7H aha
. ti _\ .NL

HMHJNW
COHHOSUOLm

m
(K

eHame

m.mm mm.:
O.Hm mm.d
scam H9:
B.N0 Om.d
o.mw m¢.i
s.Hm Me.e
4\.&mu BAH.+H
Huboihmm .QWI
mmoam mmco

 

-134-

The average error for all twenty-eight cases is 1.3 per-cent. Evident-

ly, relatively accurate slope estimates may be obtained on the basis of

a limited quantity of a product.
Another indication of the accuracy in estimates may be obtained from

using the estimated slope to project man-hour values for greater quantities.

The estimated cumulative average man-hours per unit are shown in column

eight of Table 6.1. These values were obtained through the extension of

the line computed for the limited quantity of units. The size of the

actual error is given in column ten of Table 6.1

 

 

 

ABLE 6.2
FREQUEICI DISTRIBUTIOF 0F ERROR I] ESTIKATE
Size of Error in Per—Cent No. of Cases Per—Cent of Cases

0 to 2.99 24 40.3
3 to 4.99 11 20.4
5 to 6.99 6 11.1
7 to 9.99 4 7.4
10 to 12.99 6 11.1
13 to 16.99 1 1.8
17 to 20.99 1 1.8
21 to 2h.99 i .6
54 100.0

Table 6.1 indicates that the size and the direction of error may

vary at different quantities. An error in estimate was computed at

fifty-four points of the twenty—eight cases. In other words in many of

the cases the error was computed at two quantities. Table 6.2 presents

the distribution of errors. It is found that in 72.3 per—cent of cases

the error is less than 7 per—cent, in 90.3 of cases the error is less

than 13 per—cent. However, in 7.h per—cent of cases the error (in h

cases) range is from 20 to 25 per—cent. In six cases the cumulative

average value was converted into unit data and compared to actual unit

hours. The error in estimate of the unit values is only slightly

-155-
greater. The increase in error was well within 2 per-cent of the error
in cumulative average hour estimates.
Summary and Conclusions

Chapter 6 was devoted to the analysis and discussion of the magnitude
of variation in the rate of time reduction of the fifty—four empirical
time reduction functions. Problems of forecasting the applicable rate

‘

of time reduction were considered and the possibility of estimating slope
on the basis of an initial quantity of units of a product was explored
in detail. Using the estimated slope of the time reduction curve, man—
hour projections for various quantities were made, and the resulting error
indicated.
First, the computed time reduction curve slope tends to vary among
firms manufacturing similar products, non—similar products manufactured
by one firm, and also models of a basic product type manufactured by one
firm. In every category the variation in slope is in excess of 6 per-cent.
This amount is judged to be excessive for forecasting man—hour requirements.
It should not be concluded from the preceding that past experience
is of no value in estitating. Past experience is most valuable providing
it is recorded and analyzed in sufficient detail to establish relation-
ships. It appears that the high variation in slope which was found in
present data is at least partly due to the fact that we have assumed that
know how and learning were comparable for all products and models when
the production program was started. To the extent that previous learning
of various degrees was present at the time production started, we may
expect the slope of individual models to vary. If proper adjustments in

the data are made, a greater uniformity of slope should be obtained.

Second, a method of estimating slope percentage after a certain

-156.
number of units have been manufactured is proposed and should yield satis—
factory results in most cases. This mathematical method of estimating
slope is of doubtful value in cases where the number of units to be pro—
duced is small or where the index of correlation for the early units is
low. Under these circumstances it would be difficult to predict the slope
characteristic sufficiently early to be of value in forecasting.

Third, estimating the rate of time reduction on the basis of three
to five initial man—hour values (plot points) at various quantities pro—
duces a relatively close approximation of the actually experienced rate.
The average error in slope estimate for all cases is 1.8 per-cent. The
largest error was h.5 per—cent.

Fourth, the rate of time reduction estimated in this manner was used
in forecasting man—hour requirements of follow—on product quantities. Com—
parison of estimated and actual direct man—hours for twenty-eight products
indicates that the error in estimate, at various quantities of production,
is less than 7 per—cent in 72.3 per—cent of cases. In 90.3 of the cases the
error is less than 13 per-cent. However, in 7.4 per—cent of the cases the
error ranges between 20 and 24 per—cent.

he conclusions of this Chapter and Chapter 5 are limited by the
fact that data were obtained from three manufacturers only. However,
man—hour requirements of five production programs and fifty-four products
were studied.

In Chapter 7, factors which are judged to have an important influence

on time reduction curve characteristics will be discussed briefly.

 

CHAPTER VII
SOEE FACTORS AFFECTITG SLOPE
Introduction

There is a large number of factors that affect the time reduction
curve characteristics. An intensive analysis of the nature of these
factors would be desirable, but is beyond the scope of this investiga-
tion. No attempt will be made to determine the relative importance of
the various factors or their effect on time reduction. It appears
pertinent to discuss a number of variables which are judged to be
important in their influence on man—hour requirements.

The following discussion is based on information which was ob—
tained from interviews held with personnel of the three firms, and
some published material available.
fanual Dexteritx and Group Skills

The importance of workers as a group and as individuals should
not be overlooked in any manufacturing time reduction scheme. The
data obtained from firm C, shows that the decrease in man—hours for
one of the models continues to take place after nine years of produc—
tion (see Figure 4.17, printing press No. 7), and after cumulative
output has reached close to one thousand units. In Chapter 2 it was
stated that most of the experiments on the acquisition of skills tend
to support the proposition that a plateau is reached in learning an
industrial task. It should be added that these controlled experiments
were of relatively short duration (less than six months). There is

no general agreement on the shape of an individual learner's curve

-157-

 

~r‘

-190-
over longer periods of time. At this time it is impossible to state
how much of the time reduction contained in the time reduction curve
should be credited to worker's learning. It may well be that the
high percentage of time reduction per unit experienced at the initial
stages of a production program is due to workers' learning.

In connection with learning on the part of production employees,
some troublesome questions are raised when an attempt is made to
determine what influence, if any, learning has on future manufacturing
time reduction. It is reasonable to assume that in manufacturing there
are always some operations which are similar or identical to those
performed in the past. It may be expected that in those cases where
similarity or change is accurately estimated and incorporated in the
adjusted time reduction curve, this problem will be minor.

0n the other hand, there are certainly some operations, riveting
for example, where it is not at all reasonable to assume that as far as
improvement is concerned, the organization is on the 5th or 50th unit,
where in fact, the operation has not changed in the last 5,000 units.

In other words, although a plant's production program of a particular
item may be in its early stages on the time reduction curve, many of

the parts and perhaps even subassemblies used in production may be at an
advanced stage which on the man—hour per unit basis will aproximate a
constant level. Because of accumulated learning, it should be emphasized
that the time reduction curve technique cannot be applied without regard
to previous manufacture of similar products. Obviously, learning on the
part of the workers carries over from one product to the next. How

can this be explained in view of the empirical data on the shape of

(o

 

-159-

he time reduction curve? It seems that the foregoing substantiates
the view that in an experienced facility the improvement rate is
primarily a result of management and methods improvement. Also,
although it may be useful to know the exact amount of previous learn—
ing, his is not essential for working purposes, nor has a usable
method been developed to measure such.

Some Long Range Factors

 

There are a number of factors which may be found existing in a
firm, and which are probably responsible for some of the variation in
Slope. For example, firms A and B have manufactured small electronic
components, which are somewhat similar yet the variation in slope is
considerable. Some qualitative factors which in the past have been
reported to have an influence on man-hour consumption will be discussed.
These are termed long-range because it is assumed that it takes an
extended period of time to develOp these manpower attributes.

A number of studies have shown that morale and motivation on one
hand, and workers'productivity on the other, are positively related.

The Hawthorne works study at Western Electric, perlormed by Roethlisberger
and others seems to indicate that morale and attitude are important to
productivity.1 Since this pioneering effort, others have come up with

similar results.

 

ll ., , . v
r. J. Roethlisoerger and d. J. Dickson, Lanagement and the

worker, (Cambridge: Harvard University Press 19507.

 

"b

(' l ' ' 1' H V 1

Artnur d. Brayfield and Halter n. Crocket, "employee Attitudes
and Employee Performance,” Psychological Iulletin, (September, 1955),
pp. 396—h24.

 

-160-

When an organization has a sound suggestion system, all employees
may participate in the improvement effort, and this should result in
greater production efficiency. Studies have shown that employees can
make suggestions that improve machines, develop new devices, procedures,

3

and techniques that result in more efficient production. The number
of shifts that a firm operates will also affect the time reduction
curve. It was found that the slope of the time reduction curve for
second and third shift operations is not as steep as for the first
shift because the latter shifts are less efficient. As a rule of
thumb, a number of airframe manufacturers use ten, eight and six as

a
indices of efficiency for first, second and third shifts. Therefore,
we may expect the time reduction curve to be flatter on a multishift
plant as compared to a single shift operation, though the item pro—
duced and all other things are assumed to be equal.

Turnover of production personnel is very expensive in terms of
production lost and low initial output of a new employee. While some
turnover is not avoidable, excessive turnover rates in a specific
plant may cause he SIOpe of the time reduction curve to be flatter
than in cases of low turnover percentage.

The above discussion deals with only a few of the more obvious

manpower management factors that affect the production efficiency and

therefore both the slope and the position of the time reduction curve.

 

3J. L. Rimes, "Suggestion Schemes——A Summary of the Literature,"
Industrial Psychology and Personnel Practice, Vol. 8, ho. l, (harch,
19555. pp. 27-35.

Information obtained from several airframe companies.

-161-

This discussion is brief because the material is covered in greater
detail in sources indicated.

The engineering departments may influence the rate of improve—
ment in several ways, both before actual production gets under way
and during production. This includes clarification of drawings,
clarification of engineering errors, simplification in designs, and
normal development of new techniques. Often in the case of various
high priority programs, production commences long before the model is
engineered for mass production. Thus, production exceeds engineering
provisions and thereby results in relatively flat time reduction curve
slope. The quality of engineering liaison with the production organ-
ization will also affect the rate of improvement.

In addition to design engineering, the activities of the indus-
trial engineering department play an important role. Time and motion
study may be expected to have a direct influence on the number of
man—hours required. hethods analysis, systems and procedures improve—
ments, and development of manufacturing aids will bear on time reduc—
tion.

The production control functions are all important to a smooth
operation of all production phases. Dispatch, planning, routing,
shoploadi g, and the general efficiency of operating controls is
required. Tooling is another factor that is often mentioned in
connection with the rate of improvement. Occasionally production
starts with temporary or low production tools. It may be expected
that these tools will require extensive maintenance attention and
production delays. Again, because of great demand for some items it

may be necessary to start production before all tools are available.

-162-
Kodernization and automation will have drastic effects on the rate
of improvement. Recently, for example, The Toeing Airplane Company
plant in'fiichita, Kansas, installed four punched tape controlled
machines that are building relatively complex wing panels for the
B-SZG stratofortress. Only two men are required to run the new
machines replacing forty—eight former riveters.5 This type of
change that is taking place in many industries cannot help but reduce
the man—hour requirementx
Procurement of effective material sizes that minimize cutting,
handling, and scrap all enhance production efficiency. haking
certain that materials and component parts are on hand, development
of efficient sources of production, and economic use of outside
production can make a great contribution to the reduction in man-
hour requirements.
The Effect of Scale of Production
Scale of production is seldom mentioned in connection with the

ime reduction curve, and is believed to have little effect. It
cannot, however, be assumed that the rate of production has no effect
on man-hour requirements per unit. A visual examination of time
reduction curves of different facilities manufacturing like models
at varying rates, does not indicate correlation of rate of production and
slope or position of the time reduction curve. It seems that in airframe

production there are certain essential requirements in machinery and

 

Kewsweek, February 23, 1959, p. SO.

/ . .
QSource 300K, 22. Cit., Vol. II.

 

 

-163-

and equipment which do not vary in kind as rates of production are
increased. The only thing that is necessary for higher rate of pro-
duction are additional sets of equipment and machinery and, of course,
larger floor space. Ir. Hirsch comes to the same conclusion in his
study of a machine tool manufacturer. Hirsch explains this phenomenon
as being at least partly due to the fact that relatively fixed quanti-
ties of machining and assembling require relatively fixed centinatiais

7

of equipment. Kr. Asher, in a study of costs, says that there are

two costs that rate of production will affect: set up costs and the
number of subassemblies that will be used?

It seems that the volume of proeuction is of minor importance
and is overshadowed by the importance of cumulative production. These
two are of course related, in that the rate will determine the flow
time of a particular model. Our knowledge of time reduction curve at
extremely low rates is too meager to warrant any conclusions. An
examination of data obtained from firm C, to see if there is a relation—
ship between volume of output and the slope of the curve did not result
in any evidence to the affirmative.
Tan—hours Recuired and Type of Product

One of the inquiries into causes of variation in the slope of
the time reduction curve is The Acceleration of Airframe Production,

report prepared at Headquarters, Air Hateriel Command in 1947. During

 

'%4. Z. Hirsch, "hanufacturing Progress Functions," The Review of
Economics and Statistics, Vol. 34 (Kay, 1952), pp. 143-145.
3
H. Asher, 29. ci ., p. 87.
1‘

J. R. Crawford and E. Strauss, The Acceleration of Air;
Production, Air hateriel Command, Dayton, Ohio, 1947.

”‘1‘!
I‘m 19

 

 

-164-

world War II, the aircraft industry became what may be termed as mass
production enterprise. This production experience furnished an attrac—
tive opportunity for study and analysis of factors which influence the
rate of improvement in man-hours. The above report was primarily in—
terested in discovery of planning factors, which might be useful as a
guide in present and future production planning and analysis. Since
variations in the slope of the time reduction curve have a direct
influence on lead time, a number of potential causes were analyzed to
see if there was a relationship between slope and product character—
istics. To determine the influence of airframe unit weight, the
data were analyzed to see if unit weight had an influence on direct
man—hours. Plotting of direct man-hours per pound on the vertical
axis and the airframe unit weight on horizontal axis did not indicate
0
any relationship. It seemed reasonable to expect that airframe type
would influence the direct man—hours required. Samples were taken
for various types of airframes and at various unit numbers. Deviations

from the ave“age direct nan-hours oer pound for each type of plane were

L

q

IN 0 p. x r v . n r~rv1 "‘ ‘ -. ¢ ' \
lalge. A iurtner analySis of averages and GGVlSOlORS s.

Q
d
0’)
}_.
Uy 7.
:3
H o
*"3
f—J
O
:5
(+-

variances within the particular type of plane. For example, the study
of direct man-hours for fighter aircraft reveals that although the
average was relatively high, some fighter data consistently showed

lower nan—hour ranges. In each case of these low nan—hour cases,

the fi hters were manufactured by what was considered large, experienced,

L)

and well organized companies.

 

lolbid, p. 83.

-165-

The series for bombers, fighters, transports, and trainers were
plotted at selected cumulative plane numbers to compare with the
average for the industry as a whole. The bomber curve is slightly
below the industry average curve, and this may be ascribed to the fact
that in general, bomber aircraft permit greater accessibility and the
fact that this program was given top priority. The position of the
fighter curve is consistently above the industry average and this is
probably due to the fact the fighter aircraft are usually thought of
as being more complex than other types of aircraft. Also, this pro-
duction never reached the stability enjoyed by the bomber program.

The cumulative average curve for trainers starts out above the average
for all aircraft and then drops below average, and finally, rises

above it at the conclusion of the war. In part, this behavior may be
explained in that no mass production assembly line methods were employed
at first. The urgency of early pilot training and introduction of

mass production methods accounts for the rapid improvement. As the
demand for trainers was satisfied and the rate of production declined
sharply, the improvement was less than average for all other programs.

Although the above brief analysis leaves some questions unanswered,
it indicates what may reasonably be expected, e.g. the characteristic
of an individual product will influence its own rate of improvement to
be unlike that of other units. Thus, characteristics of complexity,
accessibility, priority status, and production methods all enter into
the picture to present a partial explanation of man-hour deviations
in terms of type product.

Another attempt to explain variation from the industry average

man—hours is an analysis of the influence of comparative newness of

-166-

a particular model or facility. Each model was classified as to whether
it was new or proven, and as to whether it was produced in a new or

experienced facility. The classes which were developed are listed

below:
he. of
Class hodels in Class
(1) Proven models, experienced facility #3
(2) Proven models, new facilities 22
(3) New models, new or experienced facilities 53

Next, weighted averages of direct man—hours per pound at selected
cumulative intervals were calculated for each of the above classes.
The data indicates that the early units of proven models produced at
experienced facilities cost less in terms of direct man—hour input
than does the average for all models. As more units were produced,
this advantage was not maintained.

The new facilities consisted primarily of secondary and tertiary
producers. The new facilities curve follows industry average curve
very closely until it reaches about the middle portion of the progress
curve. Then, the savixgs that secondary sources realize, as a result
of the introduction of engineering changes already proven by the
primary source, become apparent. The production of a new model,
whether the facility is experienced or not, requires consistently
above average man—hours per unit. Production problems which arise
when engineering changes are introduced are worked out by the facility

which developed the original model. Therefore, secondary sources

 

lllbid, p. 84.

-167-

benefit from receiving changes in already known form. The indication
is strong that the relative newness of a model and facility did have
an effect on the rate of improvement.

The above tends to support findings reported in Chapter 5. There
are many assignable reasons for the significant variation in slepe,
and therefore, the industry average slope for a particular product
type is of little use for predictive purposes.
hanagement Learning

As management becomes increasingly aware of the special problems
involved in tha manufacture of a new or modified product, the perform—
ance of the basic managerial functions may become more efficient.
Kanagement may be CXpected to anticipate production problems to a
greater extent, and be prepared to deal with them in an expeditious
manner. T49 quality of management may be an important variable.
Kapecially in the introduction of new models, procedures, techniques
and general organization of work, management must take fine lead.
Summary and Cone usions

Although empirical analysis of the reasons for decline in man—
hours is not the purpose of this study, nevertheless, it seemed
appropriate to discuss some of the forces which are judged to be
important in determining time reduction curve Slope and the decrease
in man-hour requirements.

It would be all but impossible to assign a quantitative weight
to the almost endless number of possible factors that may influence

the time reduction curve. It is hoped that a shidy of the major

factors will be made in the future. At present the best approach

l4“

_l68—

seems to be to consider each individual case separately and take into

account the expected influences. here the historical shape of an

individual firm's improvement curve may be helpful. But at the same
time we must realize that history does not always repeat itself, nor
are conditions of a production situation always duplicated.

Lowever, past time reduction curve of an individual firm may be
expected to continue. In other words, although we cannot make an
objective determination of the various factors that affect the slope

of time reduction or the position of the curve on the vertical axis,

an adjusted historical curve may have most of these factors already

incorporated. In the final ana vsis management can to a lar:e extent
. J o c,

control the n gative influence of the many factors that affect the rate
of time reduction once the factors that are expected to cause produc—
tion inefficiencies become known.

As yet, empirical evidence does not indicate that all the factors
hat affect the slope of improvement or position of the time reduction
curve are known or have been discovered.

{W

In Chapter 0, the problems of time reduction curve analysis,

after a product change is introduced, will be discussed.

CHAPTER VIII

TIE PROBLEK OF DESIGN CHANGE

Introduction

 

It will be recalled that until now we have assumed that the model
is unchanged during any particular period of production and, therefore,
no allowances for change were necessary. This simplifying assumption
was necessary in order for the time reduction curve to hold true in any
given situation. The fact that absence of model changes is seldom
found needs no elaboration. Continuous change of product design is one
of the most important characteristics of our economy. An example of
this may be the consumers goods market where the annual model change is
an accepted practice, and where change in design is expected and de—
manded. In some cases even in the absence of physical change, the
manufacturers claim that the product is new, presumably in the hope
that this will increase the salesability of the product.

A great deal of variability as to the amount and frequency of
changes that are introduced during a particular fiscal year or within
a production program may be expected. Certain industrial products
undergo major change on what amounts to a continuous basis. Here the
pace of technological development is probably the most important single
factor in determining, or rather initiating, the change in design. The
extreme example of the rapidity of design change is undoubtedly today's
defense industry. In order to keep ahead of adversaries, the weapon
system design change has to be carried on a continuous basis if it is
going to be up to date in any sense of the word. In some cases, major

—169_

 

-17o-

production programs never get beyond the experimental stage and have

to be phased out before the production stage is reached. In an attempt
to accelerate some of the major weapon system programs, production has
started long before the weapon has been engineered and designed for
production. These factors make major design changes mandatory.

While the design change may make a product more saleable, or a
weapon system more efficient in terms of operational objectives, it
creates serious problems for production management attempting to fore-
cast, plan, and control operations. Frequent design changes complicate
the problem of production planning. Professor hoore in his book states:
”The problem of design change is a deterrent to broader adaptation of
the time reduction curve technique."

Admittedly, a number of techniques are used to adjust for a
product change in order that time reduction curve analysis may be
continued. However, it seems that present methods and techniques are
inadequate for a number of reasons. First, the present methods fail
to predict the time reduction after a product change is incorporated.
There is no way to determine the equivalent point on the time reduc—
tion curve after the change. Second, there is no way that we may
determine the amount of deviation, nor for that matter, to say whether
or not a deviation at all exists in a particular program after a change

has been introduced. The changed and the unchanged parts of a product will

 

1
Franklin G. hoore, Production Control (flew York: KcGraw-Hill,
1958), Chapter 9.

 

 

-171-

exhibit different time reduction velocities, with the result that
future time reduction will not be at the rate which was experienced
before the design change had been introduced. Third, unless forecast—
ing and comparative analysis can be continued even after a product
change is introduced, the time reduction curve would loose most of its
value in many cases where product changes are necessary.

In the following paragraphs we shall review the various views in
regard to transfer of skills from one task to another, review the
present methods of dealing with design changes, and finally, suggest
a new and improved method of dealing with design changes when the time
reduction curve technique is used.

Some Theoretical ASpects of Transfer

To a large extent, the problems of change that are set off by a
change in product design, are also problems of determining transfer
of skills, individual or organizational, from the old work situation
to the new one.

Thorndike is generally considered the father of contemporary
theories of transfer.2 His experimental research at the beginning of
the twentieth century resulted in the conclusion that transfer takes
place according to the existence of “identical elements" in the two
situations. The identical elements theory of transfer proposes that
the possibility of transfer depends on the presence of identical

factors in an original situation and a new situation.3 This identity

 

2Ernest R. Hilgard, Theories of Learning, (Sew York: Appleton—
Century—Crafts, 1943), p. as.

Blt‘ldo , p. 70.

of elements may be found in the content, procedure, or ideal. Thorndike

states:

. . . a change in one function alters any other only
in so far as the two functions have as factors identical
elements. The change in the second function is in amount
that due tp the change in the elements common to it and
the first.

In contrast to Thorndike, who maintains that there must be a
specific identic bond between situations, Judd proposed his theory of
generalization in which he emphasizes the importance of transfer of
general abilities.5 One must only accept a particular node of behavior

as part of his ”general principles," and it will recur even when the
situation is a new one.
Whether one chooses to support the identical elements or the

generalization theory, the concern is about the relation between two

groups of activities. As one authority points out:

It may be questioned, moreover, whether these
theories may be considered different statements ......
The elements called identical are general to the
degree that they extend beyond the situation in
which they were originally earned; they are identical
only in the sense that they belong to the same class
of events. Generalizations are also common to both
training and test situations and are, then, as identi-
cal as the features subsumed under a theory of identical
elements.

Thus, the two theories are not mutually exclusive, since both
interpret that transfer is a function of the relations between the old

and the new activity.

 

4Edward L. Thorndike, The Ehycholggy pf Learning, (Eew York:
Columbia University, 1914), p. 353.

5IIilgard, 22. 223., p. 76.

6
John A. theoch, Th2 Psrcholo. pf Human Learning, (New York:
Longmans, Green, and Co., 19475, p. 330.

 

 

-173-

The current gestaltist claim that a solution once arrived at may
be used in new situations. "Insight is often accompanied by a verbal
formula which permits the principle to be applied readily to new pro-
blems."7

There is no doubt that positive and negative transfer occurs.
Transfer effects may be defined as positive when training or experience
in one activity facilitates the acquisition of skills necessary in
another activity. Transfer may be defined as negative when the train-
ing in one activity inhibits training in another. Transfer is zero or
indeterminate when training in one has no observed effect on the
acquisition of skills required in a new situation. The vast number of
experiments have produced both negative and positive transfer, the
latter being more numerous. A few have yielded zero transfer.8 Since
the results of these experiments are already well covered elsewhere,
they will not be discussed here.9

Theories of transfer are concerned with what is retained from
the training or experience and used to facilitate learning in a new
situation. While there is a considerable amount of knowledge in exist-
ence, which describes the basic conditions of transfer, a scientific
theory which will permit satisfactory quantitative prediction is not
now available. we shall next review the various methods that are now

used by those firms where the time reduction curve has been used for

a number of years.

 

Eilgard, 23. cit., p. 194.
8I-LcGeoch, pp. cit., p. 394.

9Ibid., pp. 330-420.

-17h-

Present Industrial Kethods for Estimatinggthe Effect of Changes on thg
Time Reduction Curve

Changes in a product will affect the number of hours required to
produce that product and therefore the slope and also the position of
the time reduction curve. The time reduction curve will have to be so
constructed as to reflect these changes. But even more important is
the fact that it must be so constructed as to enable analysis and
prediction of the path that the time reduction curve will take.

Figure 5.1 illustrates the cumulative average time reduction
curve derived from data in production of product X. The hypothetical
data is contained in Table 8.1. When changes in design are made at
customers' request, the effect of these changes on costs, as well as
many other aspects of production, have to be forecasted. As far as
the cost in man—hours is concerned, there are two elements that have
to be dealt with. The first is the cost of the design change which
includes the cost of the additional work that has to be performed as
a result of this change, less the cost of the work that has been
deleted. One of the alternatives available to us is, of course, to
plot the actual data as it accrues and disregard the design change all
together. Figure 5.1 indicates the shape of the time reduction curve
without any adjustment for the design change. It shows a sharp rise
in the shape of scallops at unit one hundred and one where the change
was introduced. At unit one hundred and one, the projection along
the original curve to forecast the next unit would be quite meaning-
less. Also, any projection of the data of the additional units would

fail to indicate when actual production would again reflect the

-l75

TABLE 8.1

MAN—HOUR DATA ADJUSTED FOR PRODUCT CHANGE*

 

 

Total
Man—Hours Man-Hours Man-Hours Man-Hours
Per Unit Per Unit Per Unit Per Unit
Original Part A Part B After Composite
Unit No.1 Estimate, (Unchanged) (Changed) Change Unit K6._
1 1000.0
64 262.1
100 227.1
101 226.3 113.2 500.0 613.2 4.7
102 225.6 112.8 400.0 512.8 ’ 8.2
103 224.9 112.5 351.0 463.5 11.5
104 224.2 112.1 320.0 432.1 14.0
105 223.5 111.8 298.0 409.8 16.5
110 220.2 110.1 238.3 348.4 27-8
125 211.3 105.7 177.4 283.1 53.5
175 189.6 94.8 124.6 219.4 115.0
230 173.7 86.8 104.3 191.2 185.0
350 151.7 75.8 84.5 160.3 320.0
400 145.3 72.5 79.5 152.0 390-0
600 127.5 63.7 67.5 131-2 600-0
1000 108.5 54.5 55.9 110.4 1000.0
* SOURCE: Hypothetical data

h.-. g—o... ..

Wu»--.

~-....... - .

»,_

1271:?

 

 

 

iricl

III-'1
‘Ill

111'.

~.--I\.-.,L.Ltf.\. ..t.t.~.-...,i\ .11» Titlirsi .
. .. itiiLl-W... - -Ll- ....... -.. UTT

lllln"
. ultti

 

 

 

 

isly
0-
me

whaméfl

 

 

-l77—

original rate of time reduction experienced for the units before the
change was introduced. It may be expected that sooner or later the
curve will fare into the original lepe, but as to when this will occur
it is impossible to state.

Because there are a number of major design changes that are intro-
duced, great difficulties are encountered in constructing useful time
reduction curves. A number of techniques have been developed tocwer—
come these difficulties. These will be presently considered.

Because the time reduction curve had been develOped in the air-
frame industry, it appeared desirable to contact a number of the leaders
in this industry to determine the method being followed in solving
problems of forecasting the effect of changes on the curve.

Individual Compggy Practice

Following, is a summary of individual company practices in the
method of estimating the effect of changes. Because certain phases of
this information are considered by those companies, which have graciously
furnished information, to be of proprietary interest to a particular
company, the names are disguised througa the use of a symbol.

Company D in estimating a major change to an aircraft, uses an
engineering estimate of the hours which are involved. The changed
work is then plotted on the time reduction curve which is separate
from the rest of the airframe. The percentage slope of the time reduc-
tion curve, that is, the new curve which is being estimated for the
changed part, is estimated by evaluating factors of design materials,
method of machining, production techniques, complexity, etc. The new
work is then compared to past work performed in the plant. Unlike some

of the other companies, this manufacturer does not use the weight

-178-

comparison factor except in some unusual circumstances, but even if a
weight comparison factor is used it is still adjusted for a complexity
factor. Needless to say, judgments relative to the size of the complex-
ity factors have to be quite subjective.

Company E uses a method that is pretty much the same as the basic
method, which will be discussed below. Uanufacturer F estimates major
design changes to an aircraft by subjectively evaluating all the factors
involved in a particular change situation. Weight is only one of the
factors which are considered. The company reports that in incorporating
a change, special problems often arise in meeting specifications. These
would not be reflected if man—hours were estimated on a weight compar—
ison basis. It is also stated that many changes require little or no
structural modification, and these usually will show very little weight
change. Once the design change man—hours have been derived, a separate
time reduction curve is projected for the changed part.

Company C estimates the cost of a major change by developing a
detailed bill of materials for the added and deleted work. Han—hours
are estimated for all of the Operations at the one thousandth unit.
This basic labor hour estimate is then adjusted to include special
factors such as complexity. After the individual curve is constructed
for the change at unit one thousand, the work is estimated to start at
a subjectively determined unit which is usually not unit number one.
The management of company G feels that there is a carry over of learn—
ing between the unchanged work and the changed work so that there is
no need for going back to unit number one. It should be recalled that

this is a departure from the practices of some of the other manufacturers

 

-179-

under discussion here.

Company H method of estimating a major engineering change is
similar to the methods followed by other airplane manufacturers. The
company uses the weight comparison method. The unchanged weight of an
airframe is projected from the unit number at which change is put into
effect. In other words, if the effective point of a design change is
unit one hundred and one, then the company would normally project the
unchanged work also as unit number one hundred and one. On the other
hand, the changed portion of work is projected as unit number one.

This method makes the separation of the various components for accumul—
ation of time data mandatory. Projection for the changed and unchanged
portion of work is at the same slope time reduction curve which was
experienced before the change was introduced.

A somewhat unusual procedure which is being followed by this
manufacturer H may be found in that this manufacturer adds a disruption
factor to the unchanged work. The management of this company feels
that when a change is introduced the whole production process is dis—
rupted from its normal efficiency. The mere fact that the changed work
starts at unit number one does not adequately compensate for this dis-
ruption. It should be remembered that the disruption factor is to a
large extent a subjective evaluation of the effect that the change will
have on the remaining unchanged work. To obtain the unit time the
company adds unchanged and changed work.

Firms J, K, L, and M, use a method which is very similar to the
basic method to be discussed below and, therefore, will not be repeated

here.

—180_

The various methods employed in estimating the effect of a major
engineering change have been briefly discussed. (The term major is in
itself not well defined, Company J, for instance, defines a change as
major if its cost is one hundred hours or more.) There is one common
denominator in use by the manufacturers which were surveyed. This is
found in the fact that aside from the minor variation, all companies
project the changed portion of the work separately, and then add the
changed portion at specific unit number to unchanged portion of the
work to get the total unit time. There is a considerable variation in
the choice of the lepe that is being made for the changed portion of
the work. Also, the majority of the firms project the changed man-
hours at unit number one. The practice is not universal. At least
one manufacturer feels that there is enough transfer of learning from
the old to the new, to justify consideration of the changed portion
as being other than unit number one in the sequence.

Another point of departure in practice is the method employed by
some companies of adding a contingency factor which is over and above
the estimated change hours at unit number one. There is no agreement
at this point among the several users, but it appears that the estimates
for the disruption, or complexity factors, do contain a large amount
of subjectivity.

The major difference in estimating the effect of major changes is
found in the method of estimating the change hours. The firms surveyed
are split about even, with about half using the weight comparison
factor method, while the rest use what may be called industrial engin—

eering estimate of man-hours. In the case of the former, the weight

-181-

of the changed portion of the work is estimated, then past experienced
time at specific unit numbers is applied to the estimated weight. The
latter method does not consider weight of the changed work, but rather
concentrates on the operations involved. While no definite conclusions
can be made as to the desirability or accuracy of either method, it
appears that the time estimate for each new operation is the more
desirable method for a number of reasons.

First, in a situation where technology and complexity are advanc—
ing rapidly the weight change is not an accurate indicator of the work
which has to be performed. Second, certain changes require very little
or no change in weight (for example specification changes), yet increase
the amount of work that has to be performed. This is also true in a
case of equipment changes. Another variation of these methods that was
discussed is that used by Company F, which considers all the factors
bearing on a particular change. Further inquiry as to how the various
factors are weighed did not result in illuminating answers.

One of the surprising aspects of this survey was the amount of
latitude and variation found in the practice of the firms under con—
sideration. This suggests that possibly there is more than one way
to arrive at the solution to the problem of estimating the effect of
the major engineering change. It also suggests that there is no
exact scientific method that can be readily applied to this problem
and that at best the present methods need a considerable amount of
judgment and knowledge of a specific situation before they can be
used with a great deal of confidence. Next, a method for estimating
the effect of design changes which seems correct from the logical as

well as useful from the practical standpoint in dealing with change

-182-

TABLE 8.2

SUIIIRY OF TETHODS OF ESTIWLTIFG THE “FFECTS OF CEAHSE

4.4..

 

BASIS FOR UNIT NTHBER AT
”3“ CONT HGEXCY ESTI“ETIHO TIE WHICH THE CHANGED
CO;.aJY FACTOR CIKTZE PERCEYTAGE WORK IS PROJECTS:

D Yes Estimate of time No. 1
required for added
work

D Yes Uses both methods Usually ho. l with
de ending on the occasional variat-
situation ion

F No Evaluated all No. 1
factors affecting
change

G Yes Estimate of time Variable
required for added
work

H Yes weight Comparison Ho. 1

I Yes Height Comparison No. l

J No Height Comparison No. l

K Yes Estimate of time re- No. l
quired for added work

L do Weight Comparison No. 1

T7 N0 Estimate of time re- Variable

quired for added work

_133_
problems of the time reduction curve will be presented.
A Kethod for Estimating the Effects of a Najor Product Chaggg

Uhen a major change in the product is made a number of problems
in forecasting man—hours will arise. Depending upon the extent of
the change, the time reduction curve will assume a non—linear shape.
Figure 5.1 shows the shape of the curve when a 50 per—cent change is
introduced at unit number one hundred and one. The broken line in
Figure 5.1 indicates the line of the curve if there was no change.
Forecasting along this previously established trend would be hazardous
and inaccurate. Because of the change in the work pattern the previous
rate of time reduction should not be expected to continue.

In deciding whether a product cha ge merits the analyst's atten-
tion the significance of the change, in terms of the effect on man-
hour requirements, must first be determined. As yet there is no
completely satisfactory standard which would make a distinction as to
whether a product change should be termed major or minor. For the
purpose of this study a major change is defined as one which causes a
5 per—cent change in total man-hour consumption.

Once a decision is made as to whether a change is major or minor,
the treatment of the change will differ. hinor changes are usually
ignored. The justification for this treatment of the minor changes
is that a change of this type will not have an important effect on
the expected trend of the time reduction curve. his was found to be
true in connection with firm C data discussed in Chapter 4 of this

study. The incorporation of numerous, but minor, changes over a

 

_1§h_
period of several years did not result in undue instability in the
linear trend.

Clearly, if the time reduction curve is to have value it must
be useable in the following tasks: (1) Forecastin in the usual manner
and with a single curve for a product as a whole. (2 Indicate the
immediate effect of the change on the previously forecastcd man—hours,
and, (3) indicate at what quantity the effects of the change will be
overcome and the linear form of the time reduction curve may again be
used for estimating purposes.

It should be stated that the present methods may be used to fore—
cast man—hours after a change in product is incorporated. The short—
comings are in that in using the reviewed method it is mandatory that
there be separate reporting of man—hours required by the changed and
the unchanged parts of a product. Furthermore, if the changes are
numerous and major, the task of separate reporting and forecasting of
man—hours becomes difficult and perhaps unmanageable. This elaborate
procedure is unnecessary when the composite curve is used. In the
following paragraphs this simplified method is presented.

For the purpose of illustrating a method of dealing with major
product changes a hvpothetical case of the Z firm will be considered.
The Z firm is engaged in the manufacture of electronic equipment.
Although the firm has a history in electronic work, the order for one
thousand units of product X is considered new work for this firm. One
thousand man—hours were required to produce the first production unit

of ", and it was established that the time reduction curve was applicable

 

 

-135- 5
to the proposed production. 1
Column 2 of Table 8.1 gives the forecasted man—hours required to ‘
produce the quantity of units on order. It was decided that an 90 per-
cent time reduotion curve slope will be used.
Shortly after production of product I started.the customer informed
firm Z that a major change was mandatory and effective at unit one
hundred and one.
After a thorough study of the new design, the company's industrial
engineering department decided that the incorporation of this change
would result in the revision of approximately 50 per-cent of the man—
hours necessary to produce the assembly. Column 3 Table 8.1 shows the
unit man—hours for he unchanged portion of the product. Since the
change amounted to 50 per—cent beginning with unit one hundred and one,
the unchanged work would require only 50 per-cent of the time that it
would normally require for a 100 per—cent completion of the product
at that point. The unchanged portion of product X will be referred
to as part A.
The man—hours per unit on the changed portion of the work are
shown in column 4. Since there was a 50 per—cent change, the one
hundred and first unit was estimated to cost half of the original
first unit which amounts to five hundred man—hours. In other words,
the changed portion of the work would have to go back to unit number
one and be projected from there. The changed portion of product X
will be referred to as part B.
To obtain the total man—hours per unit to produce product X

after the change has been made, columns three and four should be

inc-.-
--p-

«.4»..-

“Hr—o -

few-4.

 

 

w 5.3

 

 

ll‘l
I I ll. iltl
llllll I”!
II I‘ II

nu,“-

mun-.m-

 

       
 
 
      

 

 

nun» 5;:

unallrJA . t a .4 ‘ .
W tbfllvlllll.m. H . -. ,
L ESJIIIXJIHXEJ) 4 . ~
5 htéujlp ,1)» ‘n _ ~ . _, -
0 ml: '11. “1025' ~ '. ,
1. Vanilillliwrtv ,. -
1° ‘
C:
59
.-

 

 

 

      

I Q '
ll )C

  
    

    

nip. 1
Hum» ,

 
 

‘ K]
95“}!
I II 'I

 

III!
E
"l

Illa:

II Iiinuus
II. lull

_139-
.ned. The total man—hours per unit are given in column five.

The above may be presented in graphical form. Figure 5.2 shows
the time reduction curve for part 3 of product K. The first unit of
the changed part B will require five hundred man—hours and is projected
as unit number one. Figure 5.3 gives the man—hours required to produce
part A of product X, and is projected from unit one hundred and one.

What is the equivalent unit number of experience that firm Z will
have when unit (changed) one hundred and one is produced? In other
words, at what point of the original man—hour estimate will unit one
hundred and one fall? The answer to these questions may be found in
Figure 5.4, (page 133).

Table 8.1, column five shows that unit one hundred and one will
require six hundred and thirteen hours. This amount is equivalent to
about b.7 units on the composite curve (Figure 5.@). The composite
curve is identical to the curve originally estimated for product K.

It will be noted that unit one hundred and two does not equal
5.7, the next consecutive number, it equals to about 3 units on the
composite curve. The reason for this is that the amount of time
reduction is different for part A from that for part B. Part 3 (new
work) improves more than part A. Therefore the unit at which the
change becomes effective cannot be considered as unit number one or
unit one hundred and one. Actually it is somewhere between those two
numbers. The composite number indicates the approximate location on

the original curve in terms of man-hours required. This means that

until the effects of the change have been overcome, part A and B of

—lGO_
product K m st be projected seprrrtely. however, extended use of this
approach is impractical for several reasons stated above.

How many uni 8 must be produced before the ef-ects of a change in
product have been overcome? when can the composite curve be used to
forecast man—hours in the usual consecutive manner, without resorting
to adjustments? The composite curve may be used for forecasting at that
quantity of production where the nan-hours required to produce the
changed product K approximate the original man—hours forecasted for that
quantity of units. The two values need not be perfectly equal. The
estimates developed with the time reduction curve are not so exact as to
warrant the demand that the original and the changed estimates be equal.
It is assumed that when the man-hours required to build the changed unit
equal the estimate without change, the curve may be used for forecasting
without additional adjustments.

For example: 1&5 hours are required to build 400th unit without
change. 72.5 hours are required to produce 400 units of part A (Figure
5.3), and 79.5 hours are required to produce 300 units of part E (Figure
5.2). Thus, it will require 152 hours to build unit #00 of the changed
product X. This is within 4.1 per-cent of the original estimate, and

therefore, at this quantity the curve may be used to forecast man—hours

without further adjustments.

In Chapter 8, problems created by product changes are discussed.
These problems appear to be serious, and in some cases may be a deterrent
to broader adaptation of the time reduction curve.

Theories of individual skill transfer are concerned with what is

f‘

retained from experience and used to facilitate learning in a new

-171-
situation. A satisfactory method of quantitative prediction of transfer
of knowledge of an organization is not available.

Present methods of estimating the effect of design changes, as used
by a number of major airframe firms, were reviewed. Considerable varis-
tion in practice was found.

Lajor changes will cause the tine reduction curve to deviate from its
expected trend and assume various non—linear shapes. In this form the
curve is most difficult to interpret and too uncertain to be of value in
estimating. This result is evident unless corrective adjustments are nafin.

A method of adjusting for major product changes is presented. In
using this method it is necessary that the direct man—hours for the changed

and the unchanged part of he product be projected separately. The requir-

nan-hours at specific quantities may be determined by adding the man—

Lb

e
hours of the changed and unchanged parts. The composite unit number may
be determined by locating the point at which the total average man-hours

1

per unit computed will equal to those found on the comoosite time reduc—

tion curve.

The proposed method enables forecasting after a change in product
with a single curve. It indicates the immediate effect of the change on
the original (before change) forecast of man-hours required. Finally, the
composite curve method indicates at what quantity of production the effects
of the change will be overcome, and the linear form of the time reduction

curve may again be used for forecasting.

The next chapter contains a summary an conclusions of the thesis.

CHAPTER IX
SUELATY AT: CSKCLCSIO S

In a number of the large manufacturing concerns the time reduction
curves is used as an important tool in the forecasting of direct man—
hours required in production. The time reduction curve is designed to
express the relationship between direct man—hours used in the manufacture
of a given unit of product and the cumulative total quantity that has
been produced.

The conventional formulation of the time reduction curve theory is
based on the hypothesis that the cumulative average direct man—hours per
unit decline at a constant percentage every time the quantity of units
manufactured is doubled.

This relationship results in a hyperbolic function when plotted on
arithmetic scale. In this form the curve is difficult to interpret.
ihe same data when plotted on logarithmic scale results in a linear
function.

An indication of importance of the time reduction curve may be
inferred from the following situations to which the curve is being
applied:

1. Most airframe manufacturers use the curve to predict man-

hour requirements of various production programs.

2. The U.S.A.F. Air Materiel Command uses the time reduction

curve to establish the expansion and mobilization potential
of productive facilities.

-192-

Ii

~193-

3. The Air Eateriel Command uses the curve to appraise con-
tractor's performance efficiency, progress, and production
dependability.

h. The Air Force and contractors use the curve in planning,
predicting and testing the feasibility of schedules.

5. Airframe manufacturers use the curve to determine floor
space and assembly tool requirements.

6. Determination of working capital requirements, cost control,
profit planning, and sub-contract pricing are some other
areas where the curve has reportedly been applied success-
fully.

7. A recent regional survey of metal manufacturers, other than
airframe, reports that 60 per-cent of the firms use the
time reduction curve relationship in forecasting.

The purpose of this investigation is to study the reliability
of the linear form of the time reduction function, proposed by‘wright,
as a tool for forecasting direct man-hours required in production.

Historical direct man-hour data, consumed at various cumulative
quantities of output, were obtained from three manufacturers. The
data represents fifty-four models, and five production programs.
Twenty-six of the products may be classified as major components of
electronic data processing systems. Sixteen units were bindery
machines, and twelve were printing presses. Because necessary

information relative to changes in the product was not available, the

data were not adjusted for design changes.

-194-

Data obtained were fitted to a straight line on logarithmic
scales through the use of the least squares method.

For purposes ()f forecasting man—hour requirements, it is
necessary that the time reduction curve contain reliability in its
linear form as well as uniformity in slope. An index of correlation
was computed for each of the fifty—four curves. It may be stated
that the resulting empirical time reduction functions exhibit remark—
able linearity on logarithmic scales. The correlation to the least
squares computed. line of regression is high. In fifty of the fifty-
four cases the index is greater than .90. The twelve printing press
cases produced an index :Jf correlation range of .97 and .99. How-
ever, it is possible to have a high index of correlation and also
high departure from linearity. Standard error of estimate is a tool
which provides a measure of reliability of basing estimates of man—
hours on the linear form of the time reduction curve. Over 8k per—
cent of the time reduction curves computed were found to be reliable,
e.g. did not exceed an arbitrarily set standard of reliability of
& per-cent standard error of estimate.

A number (i factors appear to be responsible for deviations
from linearity. Analysis indicates that engineering changes, low
level of knowledge of component performance characteristics, and
placing into production items of unproven design were some of the
major causes of deviations from the line. It would be desirable to
adjust the present data for fluctuations in man—hour consumption
which were initiated by management and which are assignable to these

actions.

_195_

The percentage slope characteristic of each of the fifty-four
time reduction curves was computed. An analysis of slope character-
istics of various models of a certain product type shows that the
variation in lepe is extensive. In every category of production the
variation in slope among models or product runs exceeded 6 per—cent.

The required accuracy will vary depending on the use to which the results
will be put. However, the variations in curve slope characteristics are
of such magnitude as to limit seriously the usefulness of slope experi-
enced on past models when determining what lepe should be used in forc-
casting man—hours of future models of a product type.

The possibilities of estimating the time reduction curve slope on
the basis of a limited initial quantity of production were explored.

A mathematical formula which gives the exact number of observations
required before slope characteristic of certain confidence may be
determined has been proposed. When this approach to the estimating of
time reduction curve slope is used, it is recommended that for the
quantity required in slope estimating, man—hour data be reported on a
per unit basis or in small lots.

This appears desirable because in cases where the data is reported
on a lot basis the quantity produced may have to be so large as to
negate most of the usefulness of the time reduction curve.

An attempt was made to estimate the slope on the basis of a minimum
number of man—hour observations at various quantities. Because most
of the available data were in lot form, it was impossible to control
fully the number of units which were used to estimate the time reduction

curve slope. In twenty-two of the twenty-eight cases it was possible

-196-
to obtain a relatively accurate forecast of the applicable slope from
three lot values. Four lot values were used in three cases, and the
remaining three cases required five man—hour values. The average error
in the slope estimate, based on minimum production quantities, for all
twenty—eight cases is 1.8 per-cent.

To determine the effect that these errors in slope would have on
estimates of required man—hours, forecasts were made for various quantities
for which actual data were available. Comparison of the estimated and
actual man—hours was made, and the error in estimate computed.

Computations were made for 28 products. Because the size and the
direction of error varied at different quantities, the error in estimate
was computed in fifty—four cases. in error in estimate of less than 7
per-cent was obtained in 72.3 per—cent of cases. In 90.8 per—cent of
cases the error was less than 13 per-cent. However, in 7.h per—cent of
the cases the error in estimate range is from 20 to 25 per—cent.

The number of factors which affect the time reduction curve is
large. There appears to be a need for a study of the major factors
which affect time reduction. At present, the best approach seems to be
to consider each individual case separately and take into account the
expected influences. Here the historical shape of an individual firm's
improvement curve may be helpful. A past time reduction curve of an
individual firm may be expected to contain a multitude of factors which
may well be expected to continue. In other words, although we cannot
make an objective determination of the various factors that affect the
slope of time reduction, a historical curve may have the majority of

these factors already incorporated.

_<97_
In the final an lysis, mtnsgement can, to a large extent, control
the negative influence of the many factors that affect the rgte of
improvement once the lgCtOTS that LTB expected to Cause preduction in~
efficiences become known. As yet, empirical evidence does not indic;te
that all the fictors that affect the slepe of time reduction or position

0

Cl the time reduction curve are known.

Significant changes which are introuuced when the product is being
manufactured may upset the original man-hour consumption forecast. It
has been suggested by some that the problem of changes has served as a
deterrent to broader adaptation of the time reduction curve technioue.

A number of airframe firms were contacted to determine the present
methods used in dealing with problems of change. All of the ten companies,
whose methods were reviewed, project the changed pattern of the work
sepzrately and then add the man—hours for new work to the man—hours for
unchanged part of the unit. A consider ble amount of v riation in
practice was evident. host of the firms use either a detailed estimate
of the time reouired for the changed part of the unit, or estimite the
weight of the changed pert. These are projected from unit number one.
In most cases a contingency or disruption factor is added. A methOd of
adjusting for changes, which is similar to methods now being used has
been presented in this thesis. The preposed method may be used to estim:te
the effect of a change on the original estimate, and to determine at what
point the effects of a change will be overcome.
Conclusions

Despite the many unsolved problems related to the time reduction

V1

curve, some positive conclusions can be drawn. evidence based on

-198-

empirical data for fifty—four time reduction functions indicates that

the following conclusions are in order:

1.

"'N

empirical data strongly suggests that the existence of the
time reduction curve phenomenon is not predicated on the use
of the curve for purposes of planning and control of men—hour
requirements in manufacturing situations.

The time reduction curve in its linear form is found to be
reliable and useful within stated confidence ranges. In all
but three cases, the data plotted on double logarithmic scales
resulted in a close approximation of a linear function on
double logarithmic scales. The average index of correlation
for all cases is greater than .95. In 34 per—cent of cases
estimates based on the linear curve were found to be highly
reliable, i.e. less then b per—cent stan ard error of estimate.
It is concluded that there is no universal rate of time reduc—
tion, and the tendency to assume that there is a basic uniform-
ity in slepe of time reduction curves for an industry is un-
werranted. In the airframe industry the 30 per—cent time
reduction curve has been erroneously accepted by some as the
generally applicable slope of time reduction. Analysis of the
computed slope characteristic of fifty-four time reduction
curves and Herld Her II bomber airframe production indicates
that the curve slope tends to vary widely among firms man—
ufacturing similar products, non—similar products manufactured

by one firm, and also models of a basic product type manufactured

by one firm. In every one of the above categories the variation

 

-199-
in slope is in excess of 6 per-cent. This amount of variation
in the curve slope is judged to be excessive for the purpose
of forecasting direct man—hour requirements.
Estimating the applicable slope on the basis of a limited
number of units produced results in a relatively close
approximation of th actual curve slope attained in production.
The average error in the slope estimate for all cases is 1.3
per—cent. Ian—hour forecasts based on the estimated slope were
made and appear to be moderately reliable. In 72.3 per-cent
of the cases the error in estimated man-hours is less than 7
per—cent. In 90.8 per-cent of the cases the error in estimate
is less than 13 per—cent. However, in 7.4 per—cent of the
cases the error ranges from 20 to 25 per—cent.
When the time reduction curve slope is estimated on the basis
of a limited production quantity, it appears desirable to
report the man—hour observations on basis of units or small
lots. This would make possible an earlier estimate of applic-
able slope than would be the case if man—hours were reported
on the basis of large lots.
It appears that the time reduction curve is of limited use-
fulness in cases where the total quantity to be produced is
small, and where the index of correlation between man—hours
per unit and total units produced is low in the first part of

the run. Under those circumstances it would be difficult to

predict the applicable slope percentage sufficiently early to

be of value in forecasting.

-200-/ 51 0‘

7. It is concluded that in spite of the fact that the time
reduction curve relationship is highly reliable, it is of
very limited usefulness in forecasting direct man-hours
required in the production of a product before a number of
units of that product have been manufactured. This condition
exists because of the inability to estimate the applicable
time reduction curve slope before the start of production.

It may be that future research of slope determinants will
make possible somewha more accurate curve slope estimating
ahead of actual production. However, this study indicates
that the time reduction curve is with certain limitations, a
useful tool for forecasting direct man—hours required in pro—
duction after a limited quantity of a product has been man—
ufactured. Uhether forecasting results will be of desired
accuracy will depend on the requirements of a specific situa-
tion. Indeed, before a decision is reached as to whether the
time reduction curve should be used in a specific situation,
it must first be determined whether the benefits derived
justifv the administrative cost involved.

The conclusionsof this study are limited by the fact that data
used in the primary analysis was obtained from only three manufacturers,
a though that was supplemented by certain other data reported in the air—
frame industry. The data in the primary analysis, however, did include
man—hours actually used in five production programs and the manufacture

of fifty—four products.

APPENDIX A

 

FIFTY-FOUR EIMRICAL TIE-E

REDUCTICN’CURVES

-202-

HHS: LC;

 

mefioflfimmlL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.l‘

ll.ll.aldll11ldl‘11‘..‘ J-‘

Jan: hot mLSOSCmE

.1

1

[4141‘

9 l
JI’ L
\A
C
I‘ll! I II. iYg
.
iiiiiiiiiii LII-11:8
1.1“- IVK. I,
‘
.‘I III 1 l

 

II.

N

J Afiuuj

any;

n «jauauunu..~

“il{

t

I . H ..“ulL'... 'ILHII 1| I4 J! {I

vac: Lac mLsozcmx

a I...

.Iorfl

IrluTI 1i-

.....u.>.s

 

vac: LQQ.mLSO£:mE

AN

 

 

 

 

:1306

 

 

 

 

 

 

 

 

'
)

uh
n-o

 

 

 

 

 

 

 

 

 

 

.
. _, ‘ .
._
...
..
A...
.
v .
I -lll \ y- ‘u’iurl-_ J? v - .Aflxt \ J u I i
I .v . ,
A r...-... . Z
.LI‘VOIn. .: ...
1.. .. ., . . f
. .10 41!»... . a. 4
VON — . 01. \

. . ..1 CIV.h1-5

 

..- __.__—..
‘--‘ '-

 

 

 

' ..“I—

 

.'.a

' "t' :05
“LA. ii?
‘ i If-

 

 

 

 

   

?

 

0'”
.Y
v. ‘5 Iv
.li;
‘ )

.«suu .H—J No

A
A
v

 

 

 

 

 

 

 

 

 

 

BIBLIOGRAPHY

m

Berghell, A. Bo . En . e r e . 3f 0
New York: McGraw.-Hill Book Co., Inc. , 1944.

Hilgard, Ernest R. Theories Of Learning. New York: Appleton-
Century-Crafts , 1948.

Laird, Donald A. and Laird, Eleanor C. fiagtigal Business Psycholng.
New York: McGraw-Hill Book Co., Inc. , 1956.

McGeoch, John A. The Psychology Of Human Learning. New York:
Longmans, Green, and Co., 1947.

Moore, Franklin G. Progugtlon Contrgl. Second Edition. New York:
McGraw-Hill COO, 1110., 1958.

Ryan, Thomas Arthur and Smith, Patricia Cain. 221E. giples of Indus-
W. New York: The Ronald Press Co., 1954.

Smith, Roy 14., William C. , and Horton, Henry G. Improvement, 92116
Hdeogk. Seattle, Washington: Boeing Airplane Company, 1956.

Tiffin, Joseph. t a h o . New York: Prentice-Hall,
1110., 19520

Thorndike, Edward L. Th P he 0 Of L arnin . New York:
Columbia University, 1914.

Thorpe, Louis P. and Schmuller, Allen M. W
w. New York: The Ronald Press Co., 1954.

Reports

Alchian, Armen. An Airframe Production Egg; on. Santa Monica:
The Rand Corporation, 1949.

. Reliability Of Progress Curves In Aircraft fiodugtion.
Santa Monica: The Rand Corporation, 1950.

 

Arrow, K. J., and Arrow, 8. S. Metho o o ica Prob em In ’ frame

Qgst Performance StQ;e es. Santa Monica: The Rand Corporation,
1950-

Asher, Harold. Co 1 Be at' ns ' In Th ' f we In ’0
Santa Monica: The Rand Corporation, 1956.

Crawford, J. R., and Strauss, E. N W I A a n Of
W. Dayton: Air Materiel Command, 1947.

-226-

-227-

Hoffman, F. S. Comments on the Modified Form 0; the Aircraft Pro-

,gzgsleungtlgn. Santa.Monica: The Rand Corporation, October 4,
1950-

Playnard, Bo I. 143 he a . 3. Of . . 0
Proceedings: Fifth Annual Industrial Engineering Institute,
University of California. Los Angeles, February, 1953.

Shappell, N. D. Production Application of Time Reduction gdgges.

Proceedings: Fifth Annual Industrial Engineering Institute,
Univeréity of California. Los Angeles, February, 1953.

Thus, H. W. _;m§_fieduggig__gg:1§§. Proceedings: Fifth Annual

Industrial Engineering Institute, University of California.
Los Angeles, 1953.

Unattributed. An In r V‘ Ra iona an Ma hematic ana 'on of

The Progress Quays id Airframe Production. Stanford: Stanford

Research Institute, August 10, 1949.

Unattributed. a nshi f Deter ' ‘ h 0 timum an.’ ’ it

o 1’: _‘u--£ , o_ aPea 6 .6 .° -' .0 -,_ -"‘ n 0? 8111.
Stanford, California. Stanford Research Institute, December 31,
1949.

Articles

Andress, Frank J. "The Learning Curve as a Production Tool,"

flariardiflusiasssiflszieu. JanuaryrFebruarYb 1954-

Brayfield, Arthur R., and Crocket, Walter M. "Employee Attitudes
and Employee Performance," Psxghologlcal gdlletin, September,
1955.

Bremeck, R. "The Learning Curve for Labor Hours - For Pricing,"
NAA Bdllgtin, June, 1958.

Bryan, Stanley E. "Fair Value and the Learning Curve," ,EBEQQéélfla,
September, 1954. -

Bryan, W. L., and Harter, N. ”Studies in the Telegraphic Language,"
ngghological Revleg, 1899, pp. 346-376.

Carr, G. W. "Peacetime Cost Estimating Requires New Learning Curves,"
Agiagidn,vo1. 45, April, 1946, pp. 76-77.

Chassan, Jack. "Estimating Direct Labor Requirements in Aircraft

PTOduction.“ Indus121211A1isiinn. July, 1945. PP. 56-63.

Cole, Reno R. "Increasing Utilization of the Cost-Quantity'Rela-
tionship in.Mbnufacturing," Th J a f t a ine -
lgg,.Mey-June, 1958, pp. 173-177.

-228-

Crawford, J. R. "Statistical Accounting Procedures in Aircraft
Production," A§£2_21g§§3, March 15, 1944.

Grouse, P. B. "Projecting Labor Loads in Aircraft Production,"
Aero Digggt, October, 1943, pp. 216—218.

. "Production Performance Comparison," Aero Digest,
Vol. 47 No. 5, December 1, 1944, pp. 68-123.

 

Fisher, A. M. "Estimating Future Labor Costs," Management Review.
Vol. 41, March, 1952, pp. 187-188.

Gables, C. R. "Transfer of Training and Skill Assumption in Track-
ing Tests," British arter of erimenta P cho "

1951, pp. 99'1100

Gianini, G..M. "Aircraft Cost Control," Aero Digest, Vol. 39, No. 2,
August, 1941, pp. 187&189.

Hadley, J. R. "Learning Curves on Log-Log Paper; Technique for De-
termining Learners Allowances,“ Advanced Management, April,
1950, pp. 16-17. ,

Hall, L. H. "Experience with EXperience Curve for Aircraft Design
Changes," NAA Bdlletin, December, 1957, pp. 59-66.

Himes, J. L. "Suggestion Schemes-A Summary of the Literature",

lgdngggjal Psyghologx and Persgnnel Eragtigg, V01. 8, No. 1,

Hirsch, W; Z. "Manufacturing Progress Functions", Ihfi_flfllififl_2£

Egonomlgs and Statistlgs, Vel. 34, May, 1952, pp. 143—145.

Jordan, R. B. “Learning Curves and How to Use Them," NAA Bdlletin,
January, 1958, pp. 27-39.

Knowles, A. R., and Bell, L. F. "Training Curves," Fadtorx'Manage-
.mgdt and Maintenance, June, 1950, p. 115.

Laddon, I. M. "Reduction of Man-Hours in Aircraft Production,"

Lundberg, R. H. "The Learning Curve Theory Applied to Production

Costs,9 S, A, E, JOgrdal, May, 1956, pp. 48-49.

Mensforth, Eric. "Airframe 0 tion," Aircraft Production, V01. 9,
Oct., 1947, pp. 388-395-

Middleton, K. A. "wartime Productivity Changes in the Airframe

Industry," Mggthly Labo; Review, Vbl. 61, No. 2, August,
1945. pp-.215-225.

 

 

inlill‘llllllf
{.1111

 

-229-

Montgomery, F. J. "Increased Productivity in the Construction of
Liberty Vessels," Monthly Labor Review, November, 1943,

PP 0 861”864o

Raborg, W. A., Jr. "Mechanics of the Learning Curve," Aero Digest,
NOV ember, 1952, pp. 17‘21 o

Unattributed. Newsweek, February 23, 1959, p. 80.
wright, T. P. "Factors Affecting the Cost of Airplanes," Journal

of Aeronautical Sciences, February, 1936, pp. 122—128.

Wyer, Rolfe. "Industrial Accounting with the Learning Curve," ‘lhp

Califopnia Certifipd Publig Appountant, Vbl. 33, N0. 3,

February, 1956, pp. 24P34.

Pamphletp
Anzanos, A., Field, R. M., and Lorenz, R. E. Conprapt Estimating

Pppgpesg Curves Fagtopp and Applipation. St Louis: McDonnell

Aircraft Corporation, 1958.
Blume, E. J., and Norris, R. E. In rove YOur B , North American
v Aviation, Inc., Columbus, Ohio (n.d.).

Blume, E. J. and Peitzke, Donald. Purchasing With the Learning Curve.

Columbus: North American Aviation, August, 1953.

Brown, William.F. The Improvement Curve. Wichita: Boeing Airplane
Company, March, 1955.

Crawford, J. R. Asymototic Progress Curve Tables. Burbank, California;
Lockheed Aircraft Corporation, 1945.

. Estimating Budgetlpg and Scheduling. Burbank, California:

Lockheed Aircraft Corporation, 1945.

. Learnlpg Curve, Ship Curve, Ratiop, Related Data.
Burbank, California: Lockheed Aircraft Corporation, (n.d.),
p.52.

Fowlkes, T. F. anation of Learnin Curves a A ie to Airc aft
Manufactur . Fort Worth, Texas: Convair, November, 1953.

 

 

Morgan, A. W. eri C es A ’cab e t th Aircraf In t .
Baltimore, Maryland: The Glenn L. Martin 00., 1952.

Rutan, E. A. Theogz of the Learning Qppge. Dallas, Texas: Chance

Vaught Aircraft, Inc., October, 1948.

—230_

Unpppliphed Mappplal

Crawford, J. R. "Learning Curves," unpublished manuscript, 1958
(typewritten).

Hammer, K. F. "An Analytical Study of "Learning Curves as a Means
of Relating Labor Requirements to Production Quantities",
unpublished Masters Thesis, Cornell University, September, 1954,
(typewritten).

Reguero, M. A. "An Economic Study of the Airframe Industry",
(unpublished) Ph.D. dissertation, Department of Economics,
New Ybrk University, October, 1957, (xeroxed).

Stupar,.Max. "Forecasting of Airplane Man-Hours“, unpublished
manuscript, Headquarters, Air Materiel Command, 1942, pp. 1-8,
(mimeographed).

Taylor, J. G. "An Investigation of the Shapeof Learning Curves for
Industrial Motor Tasks", unpublished Master's Thesis, Cornell

University, 1951, (typewritten).

 

 

 

10021. USE Lu...

 

 

 

"mmmm